Parsimonious mixtures of multivariate contaminated normal distributions

A mixture of multivariate contaminated normal distributions is developed for model‐based clustering. In addition to the parameters of the classical normal mixture, our contaminated mixture has, for each cluster, a parameter controlling the proportion of mild outliers and one specifying the degree of...

Full description

Saved in:

Bibliographic Details
Published in:	Biometrical journal Vol. 58; no. 6; pp. 1506 - 1537
Main Authors:	Punzo, Antonio, McNicholas, Paul D.
Format:	Journal Article
Language:	English
Published:	Germany Blackwell Publishing Ltd 01.11.2016 Wiley - VCH Verlag GmbH & Co. KGaA
Subjects:	Algorithms Cluster Analysis Contaminated normal distribution Contamination EM algorithm Mixture models Model-based clustering Models, Statistical Normal Distribution Contaminated normal distribution EM algorithm Contamination Mixture models Model-based clustering
ISSN:	0323-3847, 1521-4036, 1521-4036
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Abstract	A mixture of multivariate contaminated normal distributions is developed for model‐based clustering. In addition to the parameters of the classical normal mixture, our contaminated mixture has, for each cluster, a parameter controlling the proportion of mild outliers and one specifying the degree of contamination. Crucially, these parameters do not have to be specified a priori, adding a flexibility to our approach. Parsimony is introduced via eigen‐decomposition of the component covariance matrices, and sufficient conditions for the identifiability of all the members of the resulting family are provided. An expectation‐conditional maximization algorithm is outlined for parameter estimation and various implementation issues are discussed. Using a large‐scale simulation study, the behavior of the proposed approach is investigated and comparison with well‐established finite mixtures is provided. The performance of this novel family of models is also illustrated on artificial and real data.
AbstractList	A mixture of multivariate contaminated normal distributions is developed for model-based clustering. In addition to the parameters of the classical normal mixture, our contaminated mixture has, for each cluster, a parameter controlling the proportion of mild outliers and one specifying the degree of contamination. Crucially, these parameters do not have to be specified a priori, adding a flexibility to our approach. Parsimony is introduced via eigen-decomposition of the component covariance matrices, and sufficient conditions for the identifiability of all the members of the resulting family are provided. An expectation-conditional maximization algorithm is outlined for parameter estimation and various implementation issues are discussed. Using a large-scale simulation study, the behavior of the proposed approach is investigated and comparison with well-established finite mixtures is provided. The performance of this novel family of models is also illustrated on artificial and real data. A mixture of multivariate contaminated normal distributions is developed for model‐based clustering. In addition to the parameters of the classical normal mixture, our contaminated mixture has, for each cluster, a parameter controlling the proportion of mild outliers and one specifying the degree of contamination. Crucially, these parameters do not have to be specified a priori, adding a flexibility to our approach. Parsimony is introduced via eigen‐decomposition of the component covariance matrices, and sufficient conditions for the identifiability of all the members of the resulting family are provided. An expectation‐conditional maximization algorithm is outlined for parameter estimation and various implementation issues are discussed. Using a large‐scale simulation study, the behavior of the proposed approach is investigated and comparison with well‐established finite mixtures is provided. The performance of this novel family of models is also illustrated on artificial and real data. A mixture of multivariate contaminated normal distributions is developed for model‐based clustering. In addition to the parameters of the classical normal mixture, our contaminated mixture has, for each cluster, a parameter controlling the proportion of mild outliers and one specifying the degree of contamination. Crucially, these parameters do not have to be specified a priori , adding a flexibility to our approach. Parsimony is introduced via eigen‐decomposition of the component covariance matrices, and sufficient conditions for the identifiability of all the members of the resulting family are provided. An expectation‐conditional maximization algorithm is outlined for parameter estimation and various implementation issues are discussed. Using a large‐scale simulation study, the behavior of the proposed approach is investigated and comparison with well‐established finite mixtures is provided. The performance of this novel family of models is also illustrated on artificial and real data. A mixture of multivariate contaminated normal distributions is developed for model-based clustering. In addition to the parameters of the classical normal mixture, our contaminated mixture has, for each cluster, a parameter controlling the proportion of mild outliers and one specifying the degree of contamination. Crucially, these parameters do not have to be specified a priori, adding a flexibility to our approach. Parsimony is introduced via eigen-decomposition of the component covariance matrices, and sufficient conditions for the identifiability of all the members of the resulting family are provided. An expectation-conditional maximization algorithm is outlined for parameter estimation and various implementation issues are discussed. Using a large-scale simulation study, the behavior of the proposed approach is investigated and comparison with well-established finite mixtures is provided. The performance of this novel family of models is also illustrated on artificial and real data.A mixture of multivariate contaminated normal distributions is developed for model-based clustering. In addition to the parameters of the classical normal mixture, our contaminated mixture has, for each cluster, a parameter controlling the proportion of mild outliers and one specifying the degree of contamination. Crucially, these parameters do not have to be specified a priori, adding a flexibility to our approach. Parsimony is introduced via eigen-decomposition of the component covariance matrices, and sufficient conditions for the identifiability of all the members of the resulting family are provided. An expectation-conditional maximization algorithm is outlined for parameter estimation and various implementation issues are discussed. Using a large-scale simulation study, the behavior of the proposed approach is investigated and comparison with well-established finite mixtures is provided. The performance of this novel family of models is also illustrated on artificial and real data.
Author	Punzo, Antonio McNicholas, Paul D.
Author_xml	– sequence: 1 givenname: Antonio surname: Punzo fullname: Punzo, Antonio email: antonio.punzo@unict.it, antonio.punzo@unict.it organization: Department of Economics and Business, University of Catania, Catania, Italy – sequence: 2 givenname: Paul D. surname: McNicholas fullname: McNicholas, Paul D. organization: Department of Mathematics and Statistics, McMaster University, Hamilton, Canada
BackLink	https://www.ncbi.nlm.nih.gov/pubmed/27510372$$D View this record in MEDLINE/PubMed
BookMark	eNqNkTtvFDEURi0URDaBlhKNREMzi1_Xni0hgk1CHkTaiNLyeDySl7EdbA8k_54ZbdgiTajs4px7db_vCB2EGCxCbwleEozpx9b57ZJiAhgTzl-gBQFKao6ZOEALzCirWcPlITrKeYsxXmFOX6FDKoFgJukCrb_rlJ2PwcUxV97dlzHZXMW-8uNQ3G-dnC62MjEU7V2Y_l0VYvJ6qDqXS3LtWFwM-TV62esh2zeP7zG6_fplc3JaX1yvz04-XdQGMLC664wxjeTAQUiDsbAAUvTWtoZRqvsWgEvTCQKyM1SYnoFtLZjVSnMuoGHH6MNu7l2Kv0abi_IuGzsMOtjpAkUaLthKArD_QNmECU7FhL5_gm7jmMJ0yExx2UjZzLvfPVJj622n7pLzOj2of2lOwHIHmBRzTrbfIwSruS4116X2dU0CfyIYV_QcaEnaDc9qf9xgH55Zoj6fXZ4TSeZA6p02FWfv95pOP5WQTIL6cbVW385P4eZqg9WG_QWfZbex
CitedBy_id	crossref_primary_10_1007_s00362_019_01146_3 crossref_primary_10_1007_s00357_024_09480_4 crossref_primary_10_1080_10618600_2025_2495257 crossref_primary_10_1007_s00357_017_9234_x crossref_primary_10_1007_s11634_021_00476_1 crossref_primary_10_1007_s11634_023_00550_w crossref_primary_10_1080_10618600_2025_2554675 crossref_primary_10_1007_s00285_023_01961_1 crossref_primary_10_1007_s10182_021_00430_8 crossref_primary_10_1002_sim_7687 crossref_primary_10_1016_j_ecosta_2023_10_004 crossref_primary_10_1177_09622802241309349 crossref_primary_10_1016_j_physa_2020_125354 crossref_primary_10_1016_j_spl_2025_110510 crossref_primary_10_1002_sam_11653 crossref_primary_10_1002_env_2793 crossref_primary_10_1007_s00357_025_09518_1 crossref_primary_10_1002_bimj_201900248 crossref_primary_10_1038_s41598_023_44608_3 crossref_primary_10_1080_10618600_2021_1999825 crossref_primary_10_1007_s00357_023_09460_0 crossref_primary_10_1080_09524622_2024_2354479 crossref_primary_10_1007_s42979_020_0067_z crossref_primary_10_1080_10618600_2023_2184375 crossref_primary_10_1016_j_ecosta_2021_08_010 crossref_primary_10_1002_sta4_608 crossref_primary_10_1007_s11749_019_00693_z crossref_primary_10_1016_j_csda_2016_05_024 crossref_primary_10_1007_s00357_024_09470_6 crossref_primary_10_1080_02664763_2018_1542668 crossref_primary_10_1515_ijb_2020_0059 crossref_primary_10_1007_s00357_024_09479_x crossref_primary_10_1016_j_jmva_2022_105020 crossref_primary_10_1080_03610926_2024_2311795 crossref_primary_10_1007_s11634_023_00542_w crossref_primary_10_1080_00949655_2020_1805451 crossref_primary_10_1109_TSP_2021_3092373 crossref_primary_10_1016_j_csda_2018_08_004 crossref_primary_10_1111_2041_210X_13644 crossref_primary_10_1007_s11634_024_00606_5 crossref_primary_10_1016_j_insmatheco_2020_06_004 crossref_primary_10_1007_s00362_017_0964_y crossref_primary_10_1002_dys_70013 crossref_primary_10_1002_wics_1658 crossref_primary_10_1007_s00357_023_09450_2 crossref_primary_10_1016_j_csda_2018_12_001 crossref_primary_10_1080_00949655_2016_1245305 crossref_primary_10_1016_j_csda_2025_108198 crossref_primary_10_1007_s00357_016_9211_9 crossref_primary_10_1007_s11749_024_00920_2 crossref_primary_10_1007_s11634_022_00532_4 crossref_primary_10_1080_03610918_2019_1698745 crossref_primary_10_1080_00401706_2025_2497822 crossref_primary_10_1080_02664763_2018_1428288 crossref_primary_10_1007_s00357_023_09438_y crossref_primary_10_1007_s11634_023_00558_2 crossref_primary_10_1016_j_cam_2023_115433 crossref_primary_10_1016_j_csda_2020_106961 crossref_primary_10_1007_s00357_023_09445_z crossref_primary_10_1016_j_spl_2024_110058 crossref_primary_10_1155_2020_9673623 crossref_primary_10_1080_10618600_2015_1089776 crossref_primary_10_1007_s00180_020_01009_8 crossref_primary_10_1002_bimj_201800095 crossref_primary_10_1016_j_csda_2022_107496 crossref_primary_10_1007_s00180_020_01041_8 crossref_primary_10_1002_sam_70011 crossref_primary_10_1002_cjs_11308 crossref_primary_10_1007_s00357_024_09473_3 crossref_primary_10_1007_s10260_021_00578_2 crossref_primary_10_1007_s11634_019_00373_8 crossref_primary_10_1016_j_csda_2023_107909 crossref_primary_10_1016_j_patcog_2019_107031 crossref_primary_10_1007_s00362_025_01723_9 crossref_primary_10_1177_1471082X19890935 crossref_primary_10_1016_j_patcog_2024_110846 crossref_primary_10_1007_s40995_018_0526_8 crossref_primary_10_1007_s00357_017_9221_2 crossref_primary_10_1016_j_csda_2022_107526 crossref_primary_10_1007_s11222_020_09950_w crossref_primary_10_1080_00949655_2018_1554659 crossref_primary_10_1177_09622802241307613 crossref_primary_10_1080_02664763_2020_1789076 crossref_primary_10_3390_a16040195
Cites_doi	10.1016/0167-7152(90)90104-F 10.1080/01621459.2000.10474285 10.1002/0471721182 10.1016/j.spl.2004.11.007 10.1111/1467-9868.00265 10.1007/s11222-011-9272-x 10.1201/9781315373577 10.1080/00949655.2015.1131282 10.1071/ZO9740417 10.1007/s00180-012-0367-4 10.1080/00949658608810872 10.1007/s00357-001-0045-7 10.1214/009053604000000571 10.1016/j.csda.2006.01.001 10.1016/j.csda.2006.10.011 10.1007/s11634-010-0064-5 10.1016/j.csda.2012.01.016 10.1007/s11749-012-0312-4 10.1016/j.jspi.2009.11.006 10.1016/0031-3203(94)00125-6 10.2307/271063 10.1198/106186005X59586 10.1080/01621459.1994.10476467 10.1111/j.2517-6161.1977.tb01600.x 10.1093/comjnl/41.8.578 10.1007/s001840100138 10.1093/biomet/88.3.767 10.1007/BF01889985 10.1016/j.jspi.2010.06.024 10.1080/10618600.2000.10474865 10.1111/j.1467-9469.2006.00505.x 10.1016/j.csda.2010.10.026 10.1007/s11222-008-9052-4 10.1023/A:1008981510081 10.1007/978-1-4614-6396-2 10.1007/BF01720593 10.1214/009053604000000940 10.1214/aoms/1177703862 10.1080/00401706.2000.10485740 10.1007/BF01886327 10.2307/2532201 10.21236/AD0620026 10.1111/j.0006-341X.2000.00483.x 10.1093/biomet/80.2.267 10.2307/2347491 10.1080/00401706.1980.10486163 10.1007/s10260-004-0092-4 10.1214/07-AOS515 10.1017/S0370164600024871 10.1016/j.csda.2009.02.011 10.1080/01621459.1998.10473711 10.1214/aos/1031833664 10.1007/s11222-010-9226-8 10.1016/S0167-7152(02)00396-6 10.1198/1061860031806 10.1080/01621459.1999.10474199 10.1016/S0167-9473(02)00163-9 10.1007/s11634-013-0139-1 10.1080/01621459.1993.10476339 10.1177/0049124188017001003 10.1109/TPAMI.2011.199 10.1137/0907013 10.1016/S0167-9473(02)00177-9 10.1214/aos/1176344136 10.1016/j.csda.2013.07.019 10.1198/106186004X12425 10.1016/j.imavis.2008.11.013 10.1111/j.2517-6161.1996.tb02073.x 10.1007/BF01908064 10.1214/aoms/1177698520 10.1007/s11634-012-0107-1
ContentType	Journal Article
Copyright	2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Copyright_xml	– notice: 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim – notice: 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. – notice: 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
DBID	BSCLL AAYXX CITATION CGR CUY CVF ECM EIF NPM 7QO 8FD FR3 K9. P64 7X8
DOI	10.1002/bimj.201500144
DatabaseName	Istex CrossRef Medline MEDLINE MEDLINE (Ovid) MEDLINE MEDLINE PubMed Biotechnology Research Abstracts Technology Research Database Engineering Research Database ProQuest Health & Medical Complete (Alumni) Biotechnology and BioEngineering Abstracts MEDLINE - Academic
DatabaseTitle	CrossRef MEDLINE Medline Complete MEDLINE with Full Text PubMed MEDLINE (Ovid) ProQuest Health & Medical Complete (Alumni) Engineering Research Database Biotechnology Research Abstracts Technology Research Database Biotechnology and BioEngineering Abstracts MEDLINE - Academic
DatabaseTitleList	ProQuest Health & Medical Complete (Alumni) MEDLINE Engineering Research Database CrossRef MEDLINE - Academic
Database_xml	– sequence: 1 dbid: NPM name: PubMed url: http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed sourceTypes: Index Database – sequence: 2 dbid: 7X8 name: MEDLINE - Academic url: https://search.proquest.com/medline sourceTypes: Aggregation Database
DeliveryMethod	fulltext_linktorsrc
Discipline	Biology
EISSN	1521-4036
EndPage	1537
ExternalDocumentID	4235533701 27510372 10_1002_bimj_201500144 BIMJ1713 ark_67375_WNG_KJH5QNT0_T
Genre	article Journal Article
GrantInformation_xml	– fundername: Canada Research Chairs program – fundername: Italian Government funderid: RBFR12SHVV
GroupedDBID	--- -~X .3N .GA .Y3 05W 0R~ 10A 1L6 1OB 1OC 1ZS 23N 3-9 31~ 33P 3SF 3WU 4.4 50Y 50Z 51W 51X 52M 52N 52O 52P 52S 52T 52U 52W 52X 53G 5GY 5VS 66C 702 7PT 8-0 8-1 8-3 8-4 8-5 8UM 930 A03 AAESR AAEVG AAHQN AAMMB AAMNL AANHP AANLZ AAONW AASGY AAXRX AAYCA AAZKR ABCQN ABCUV ABEML ABIJN ABJNI ABPVW ACAHQ ACBWZ ACCZN ACGFS ACIWK ACPOU ACPRK ACRPL ACSCC ACXBN ACXQS ACYXJ ADBBV ADEOM ADIZJ ADKYN ADMGS ADNMO ADOZA ADXAS ADZMN AEFGJ AEIGN AEIMD AENEX AEUYR AEYWJ AFBPY AFFPM AFGKR AFRAH AFWVQ AFZJQ AGHNM AGQPQ AGXDD AGYGG AHBTC AHMBA AI. AIDQK AIDYY AITYG AIURR AJXKR ALAGY ALMA_UNASSIGNED_HOLDINGS ALVPJ AMBMR AMVHM AMYDB ASPBG ATUGU AUFTA AVWKF AZBYB AZFZN AZVAB BAFTC BDRZF BFHJK BHBCM BMNLL BMXJE BNHUX BROTX BRXPI BSCLL BY8 CS3 D-E D-F DCZOG DPXWK DR2 DRFUL DRSTM DU5 DUUFO EBD EBS EJD EMOBN F00 F01 F04 F5P FEDTE G-S G.N GNP GODZA H.T H.X HBH HF~ HGLYW HHY HHZ HVGLF HZ~ IX1 J0M JPC KQQ LATKE LAW LC2 LC3 LEEKS LH4 LITHE LOXES LP6 LP7 LUTES LW6 LYRES M67 MEWTI MK4 MRFUL MRSTM MSFUL MSSTM MXFUL MXSTM N04 N05 N9A NF~ O66 O9- OIG P2W P2X P4D PALCI PQQKQ Q.N Q11 QB0 QRW R.K RIWAO ROL RX1 RYL SAMSI SUPJJ SV3 TN5 UB1 V2E VH1 W8V W99 WBKPD WIB WIH WIK WJL WOHZO WQJ WXSBR WYISQ XBAML XG1 XPP XV2 Y6R YHZ ZZTAW ~IA ~WT AAHHS ACCFJ ADZOD AEEZP AEQDE AEUQT AFPWT AIWBW AJBDE ALUQN RWI WRC WUP WWH AAYXX CITATION O8X CGR CUY CVF ECM EIF NPM 7QO 8FD FR3 K9. P64 7X8
ID	FETCH-LOGICAL-c5053-ddccc87454567c006e5576feebc322afb5547cd6157dc26cf35ebe5c99a446583
IEDL.DBID	DRFUL
ISICitedReferencesCount	84
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000387148100014&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN	0323-3847 1521-4036
IngestDate	Tue Oct 07 09:46:47 EDT 2025 Thu Oct 02 05:47:31 EDT 2025 Tue Oct 07 05:41:12 EDT 2025 Tue Apr 08 05:56:57 EDT 2025 Tue Nov 18 21:03:25 EST 2025 Sat Nov 29 06:28:47 EST 2025 Wed Jan 22 17:04:46 EST 2025 Tue Nov 11 03:32:45 EST 2025
IsPeerReviewed	true
IsScholarly	true
Issue	6
Keywords	Contaminated normal distribution EM algorithm Contamination Mixture models Model-based clustering
Language	English
License	http://onlinelibrary.wiley.com/termsAndConditions#vor 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
LinkModel	DirectLink
MergedId	FETCHMERGED-LOGICAL-c5053-ddccc87454567c006e5576feebc322afb5547cd6157dc26cf35ebe5c99a446583
Notes	istex:F803EB533857CE9AC12ADC40DE9A62BAB05C1F5C ark:/67375/WNG-KJH5QNT0-T ArticleID:BIMJ1713 Supporting Information Italian Government - No. RBFR12SHVV Canada Research Chairs program ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 content type line 23
PMID	27510372
PQID	1834787788
PQPubID	105592
PageCount	32
ParticipantIDs	proquest_miscellaneous_1846397553 proquest_miscellaneous_1835536426 proquest_journals_1834787788 pubmed_primary_27510372 crossref_primary_10_1002_bimj_201500144 crossref_citationtrail_10_1002_bimj_201500144 wiley_primary_10_1002_bimj_201500144_BIMJ1713 istex_primary_ark_67375_WNG_KJH5QNT0_T
PublicationCentury	2000
PublicationDate	November 2016
PublicationDateYYYYMMDD	2016-11-01
PublicationDate_xml	– month: 11 year: 2016 text: November 2016
PublicationDecade	2010
PublicationPlace	Germany
PublicationPlace_xml	– name: Germany – name: Weinheim
PublicationTitle	Biometrical journal
PublicationTitleAlternate	Biom. J
PublicationYear	2016
Publisher	Blackwell Publishing Ltd Wiley - VCH Verlag GmbH & Co. KGaA
Publisher_xml	– name: Blackwell Publishing Ltd – name: Wiley - VCH Verlag GmbH & Co. KGaA
References	Berkane, M. and Bentler, P. M. (1988). Estimation of contamination parameters and identification of outliers in multivariate data. Sociological Methods and Research 17, 55-64. Browne, R. P. and McNicholas, P. D. (2014). Estimating common principal components in high dimensions. Advances in Data Analysis and Classification 8, 217-226. Fraley, C. and Raftery, A. E. (1998). How many clusters? Which clustering method? Answers via model-based cluster analysis. Computer Journal 41, 578-588. Ingrassia, S. and Rocci, R. (2011). Degeneracy of the EM algorithm for the mle of multivariate Gaussian mixtures and dynamic constraints. Computational Statistics and Data Analysis 55, 1715-1725. Lo, Y., Mendell, N. R. and Rubin, D. B. (2001). Testing the number of components in a normal mixture. Biometrika 88, 767-778. Yao, W. (2012). Model based labeling for mixture models. Statistics and Computing 22, 337-347. Hartigan, J. A. (1985). Statistical theory in clustering. Journal of Classification 2, 63-76. Aitken, A. (1926). A series formula for the roots of algebraic and transcendental equations. Proceedings of the Royal Society of Edinburgh. 45 14-22. Markatou, M. (2000). Mixture models, robustness, and the weighted likelihood methodology. Biometrics 56, 483-486. Meng, X.-L. and Rubin, D. B. (1993). Maximum likelihood estimation via the ECM algorithm: a general framework. Biometrika 80, 267-278. McLachlan, G. J. and Peel, D. (2000). Finite Mixture Models. John Wiley & Sons, New York, NY. Hennig, C. (2004). Breakdown points for maximum likelihood estimators of location-scale mixtures. The Annals of Statistics 32, 1313-1340. Biernacki, C., Celeux, G. and Govaert, G. (2003). Choosing starting values for the EM algorithm for getting the highest likelihood in multivariate Gaussian mixture models. Computational Statistics and Data Analysis 41, 561-575. Dempster, A. P., Laird, N. M. and Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society: Series B 39, 1-38. Bai, X., Yao, W. and Boyer, J. E. (2012). Robust fitting of mixture regression models. Computational Statistics and Data Analysis 56, 2347-2359. Byers, S. and Raftery, A. E. (1998). Nearest-neighbor clutter removal for estimating features in spatial point processes. Journal of the American Statistical Association 93, 577-584. Schwarz, G. (1978). Estimating the dimension of a model. The Annals of Statistics 6, 461-464. Hawkins, D. (2013). Identification of Outliers. Monographs on Statistics and Applied Probability. Springer, The Netherlands. Ingrassia, S. and Rocci, R. (2007). Constrained monotone em algorithms for finite mixture of multivariate Gaussians. Computational Statistics and Data Analysis 51, 5339-5351. McNicholas, P. D. (2016). Mixture Model-Based Classification. Chapman & Hall/CRC Press, Boca Raton, FL. Raftery, A. E. (1995). Bayesian model selection in social research. Sociological Methodology 25, 111-164. Bock, H. H. (2002). Clustering methods: from classical models to new approaches. Statistics in Transition 5, 725-758. Ruwet, C., García-Escudero, L. A., Gordaliza, A. and Mayo-Iscar, A. (2013). On the breakdown behavior of the tclust clustering procedure. Test 22, 466-487. Hennig, C. (2002). Fixed point clusters for linear regression: computation and comparison. Journal of Classification 19, 249-276. Li, J. (2005). Clustering based on a multi-layer mixture model. Journal of Computational and Graphical Statistics 14, 547-568. Punzo, A., Browne, R. P. and McNicholas, P. D. (2016). Hypothesis testing for mixture model selection. Journal of Statistical Computation and Simulation. 86, 2797-2818 Aitkin, M. and Wilson, G. T. (1980). Mixture models, outliers, and the EM algorithm. Technometrics 22, 325-331. Holzmann, H., Munk, A. and Gneiting, T. (2006). Identifiability of finite mixtures of elliptical distributions. Scandinavian Journal of Statistics 33, 753-763. Banfield, J. D. and Raftery, A. E. (1993). Model-based Gaussian and non-Gaussian clustering. Biometrics 49, 803-821. Celeux, G., Hurn, M. and Robert, C. P. (2000). Computational and inferential difficulties with mixture posterior distributions. Journal of the American Statistical Association 95, 957-970. Yao, W., Wei, Y. and Yu, C. (2014). Robust mixture regression using the t-distribution. Computational Statistics and Data Analysis 71, 116-127. García-Escudero, L. A., Gordaliza, A., Matrán, C. and Mayo-Iscar, A. (2008). A general trimming approach to robust cluster analysis. The Annals of Statistics 36, 1324-1345. Ruwet, C., García-Escudero, L. A., Gordaliza, A. and Mayo-Iscar, A. (2012). The influence function of the tclust robust clustering procedure. Advances in Data Analysis and Classification 6, 107-130. Crawford, S. L. (1994). An application of the laplace method to finite mixture distributions. Journal of the American Statistical Association 89, 259-267. Campbell, N. A. and Mahon, R. J. (1974). A multivariate study of variation in two species of rock crab of genus Leptograpsus. Australian Journal of Zoology 22, 417-425. De Veaux, R. D. and Krieger, A. M. (1990). Robust estimation of a normal mixture. Statistics and Probability Letters 10, 1-7. Di Zio, M., Guarnera, U. and Rocci, R. (2007). A mixture of mixture models for a classification problem: the unity measure error. Computational Statistics and Data Analysis 51, 2573-2585. Flury, B. N. and Gautschi, W. (1986). An algorithm for simultaneous orthogonal transformation of several positive definite matrices to nearly diagonal form. SIAM Journal on Scientific and Statistical Computing 7, 169-184. Little, R. J. A. (1988). Robust estimation of the mean and covariance matrix from data with missing values. Applied Statistics 37, 23-38. Böhning, D. and Ruangroj, R. (2002). A note on the maximum deviation of the scale-contaminated normal to the best normal distribution. Metrika 55, 177-182. García-Escudero, L. A., Gordaliza, A. and Matrán, C. (2003). Trimming tools in exploratory data analysis. Journal of Computational and Graphical Statistics 12, 434-449. Hurley, C. (2004). Clustering visualizations of multivariate data. Journal of Computational and Graphical Statistics 13, 788-806. Bagnato, L. and Punzo, A. (2013). Finite mixtures of unimodal beta and gamma densities and the k-bumps algorithm. Computational Statistics 28, 1571-1597. Lo, Y. (2008). A likelihood ratio test of a homoscedastic normal mixture against a heteroscedastic normal mixture. Statistics and Computing 18, 233-240. McLachlan, G. J. and Basford, K. E. (1988). Mixture Models: Inference and Applications to Clustering. Marcel Dekker, New York, NY. Aggarwal, C. C. (2013). Outlier Analysis. Springer, New York, NY. Ingrassia, S. (2004). A likelihood-based constrained algorithm for multivariate normal mixture models. Statistical Methods and Applications 13, 151-166. García-Escudero, L. A. and Gordaliza, A. (1999). Robustness properties of k means and trimmed k means. Journal of the American Statistical Association 94, 956-969. Gallegos, M. T. and Ritter, G. (2009). Trimmed ML estimation of contaminated mixtures. Sankhyā: The Indian Journal of Statistics, Series A 71, 164-220. Davies, L. and Gather, U. (1993). The identification of multiple outliers. Journal of the American Statistical Association 88, 782-792. Karlis, D. and Xekalaki, E. (2003). Choosing initial values for the EM algorithm for finite mixtures. Computational Statistics and Data Analysis 41, 577-590. Campbell, N. A. (1984). Mixture models and atypical values. Mathematical Geology 16, 465-477. Peel, D. and McLachlan, G. J. (2000). Robust mixture modelling using the t distribution. Statistics and Computing 10, 339-348. Gerogiannis, D., Nikou, C. and Likas, A. (2009). The mixtures of Student's t-distributions as a robust framework for rigid registration. Image and Vision Computing 27, 1285-1294. García-Escudero, L. A., Gordaliza, A., Matrán, C. and Mayo-Iscar, A. (2010). A review of robust clustering methods. Advances in Data Analysis and Classification 4, 89-109. Coretto, P. and Hennig, C. (2011). Maximum likelihood estimation of heterogeneous mixtures of Gaussian and uniform distributions. Journal of Statistical Planning and Inference 141, 462-473. Verdinelli, I. and Wasserman, L. (1991). Bayesian analysis of outlier problems using the Gibbs sampler. Statistics and Computing 1, 105-117. Böhning, D. (2000). Computer-assisted analysis of mixtures and applications: meta-analysis, disease mapping and others. Vol. 81 of Monographs on Statistics and Applied Probability. Chapman & Hall/CRC, London, UK. McNicholas, P. D., Murphy, T. B., McDaid, A. F. and Frost, D. (2010). Serial and parallel implementations of model-based clustering via parsimonious Gaussian mixture models. Computational Statistics and Data Analysis 54, 711-723. Teicher, H. (1963). Identifiability of finite mixtures. Annals of Mathematical Statistics 34, 1265-1269. Yakowitz, S. J. and Spragins, J. D. (1968). On the identifiability of finite mixtures. The Annals of Mathematical Statistics 39, 209-214. Browne, R. P., McNicholas, P. D. and Sparling, M. D. (2012). Model-based learning using a mixture of mixtures of Gaussian and uniform distributions. IEEE Transactions on Pattern Analysis and Machine Intelligence 34, 814-817. Barnett, V. and Lewis, T. (1994). Outliers in Statistical Data. Wiley Series in Probability & Statistics. Chichester, UK: John Wiley & Sons. Böhning, D., Dietz, E., Schaub, R., Schlattmann, P. and Lindsay, B. (1994). The distribution of the likelihood ratio for mixtures of densities from the one-parameter exponential family. Annals of the Institute of Statistical Mathematics 46, 373-388. Ritter, G. (2015). Robust Cluster Analysis and Variable Selection. Vol. 137 of Chapman & Hall/CRC Monographs on Statistics & Applied Probability. CRC Press: Boca Raton, FL. Andrews, J. L. and McNicholas, P. D. (2012). Model-based clustering, classification, and discriminant analysis with the multivariate t-distribution: the tEIGEN family. Statistics and Computing 22, 1021-10 2010; 54 1990; 10 2013; 28 2002; 19 2013; 22 2006; 33 2000; 9 1988; 37 2002; 55 2008; 36 2000; 95 2011; 55 2010; 140 1998; 41 2001; 88 2012; 56 1978; 6 2003; 12 2004; 32 1963; 34 1995; 28 1986; 7 2000 1984; 16 1977; 39 2000; 56 1995; 25 2000; 10 1926; 45 2016; 86 2000; 62 1993; 80 2005; 71 1999; 94 1998; 93 2014; 8 2012; 22 2003; 41 2010; 4 2005; 33 1988 1991; 1 1993; 49 2012 1985; 2 2002; 5 1993; 88 2008; 18 1997; 25 1980; 22 1988; 17 1994; 89 1998 2008 2007 1994; 46 1994 2004 2007; 51 1996; 58 2012; 34 2009; 27 1974; 22 1968; 39 2009; 71 1986; 23 2004; 13 1965 2016 2015 1960 2013 2011; 141 2012; 6 2003; 61 2014; 71 2005; 14 e_1_2_11_70_1 e_1_2_11_93_1 e_1_2_11_91_1 McLachlan G. J. (e_1_2_11_72_1) 1988 e_1_2_11_32_1 e_1_2_11_55_1 e_1_2_11_78_1 e_1_2_11_30_1 e_1_2_11_57_1 e_1_2_11_74_1 e_1_2_11_13_1 Hawkins D. (e_1_2_11_53_1) 2013 e_1_2_11_34_1 e_1_2_11_76_1 e_1_2_11_95_1 e_1_2_11_11_1 e_1_2_11_29_1 e_1_2_11_6_1 e_1_2_11_27_1 e_1_2_11_4_1 e_1_2_11_48_1 e_1_2_11_2_1 Bock H. H. (e_1_2_11_17_1) 2002; 5 e_1_2_11_83_1 e_1_2_11_60_1 e_1_2_11_81_1 García‐Escudero L. A. (e_1_2_11_45_1) 1999; 94 e_1_2_11_20_1 e_1_2_11_66_1 e_1_2_11_47_1 e_1_2_11_68_1 e_1_2_11_89_1 e_1_2_11_24_1 e_1_2_11_41_1 e_1_2_11_62_1 e_1_2_11_87_1 e_1_2_11_8_1 e_1_2_11_22_1 e_1_2_11_43_1 e_1_2_11_64_1 e_1_2_11_85_1 e_1_2_11_15_1 e_1_2_11_59_1 e_1_2_11_38_1 e_1_2_11_19_1 McLachlan G. J. (e_1_2_11_73_1) 1998 e_1_2_11_94_1 e_1_2_11_50_1 e_1_2_11_92_1 e_1_2_11_31_1 e_1_2_11_56_1 e_1_2_11_77_1 Ritter G. (e_1_2_11_84_1) 2015 e_1_2_11_58_1 e_1_2_11_79_1 e_1_2_11_14_1 e_1_2_11_35_1 e_1_2_11_52_1 e_1_2_11_12_1 e_1_2_11_33_1 e_1_2_11_54_1 McLachlan G. (e_1_2_11_71_1) 2007 e_1_2_11_75_1 e_1_2_11_7_1 Gallegos M. T. (e_1_2_11_44_1) 2009; 71 e_1_2_11_28_1 e_1_2_11_5_1 e_1_2_11_26_1 e_1_2_11_3_1 e_1_2_11_49_1 Dempster A. P. (e_1_2_11_36_1) 1977; 39 e_1_2_11_82_1 e_1_2_11_61_1 e_1_2_11_80_1 Tukey J. W. (e_1_2_11_90_1) 1960 Böhning D. (e_1_2_11_18_1) 2000 e_1_2_11_21_1 e_1_2_11_67_1 e_1_2_11_46_1 e_1_2_11_69_1 e_1_2_11_88_1 e_1_2_11_25_1 e_1_2_11_40_1 e_1_2_11_63_1 e_1_2_11_86_1 e_1_2_11_9_1 e_1_2_11_23_1 e_1_2_11_42_1 e_1_2_11_65_1 Hastie T. (e_1_2_11_51_1) 1996; 58 e_1_2_11_16_1 e_1_2_11_37_1 Barnett V. (e_1_2_11_10_1) 1994 e_1_2_11_39_1
References_xml	– reference: Raftery, A. E. (1995). Bayesian model selection in social research. Sociological Methodology 25, 111-164. – reference: García-Escudero, L. A., Gordaliza, A., Matrán, C. and Mayo-Iscar, A. (2010). A review of robust clustering methods. Advances in Data Analysis and Classification 4, 89-109. – reference: Browne, R. P., McNicholas, P. D. and Sparling, M. D. (2012). Model-based learning using a mixture of mixtures of Gaussian and uniform distributions. IEEE Transactions on Pattern Analysis and Machine Intelligence 34, 814-817. – reference: Dempster, A. P., Laird, N. M. and Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society: Series B 39, 1-38. – reference: Lo, Y. (2008). A likelihood ratio test of a homoscedastic normal mixture against a heteroscedastic normal mixture. Statistics and Computing 18, 233-240. – reference: Aitkin, M. and Wilson, G. T. (1980). Mixture models, outliers, and the EM algorithm. Technometrics 22, 325-331. – reference: Böhning, D. and Ruangroj, R. (2002). A note on the maximum deviation of the scale-contaminated normal to the best normal distribution. Metrika 55, 177-182. – reference: Ingrassia, S. and Rocci, R. (2011). Degeneracy of the EM algorithm for the mle of multivariate Gaussian mixtures and dynamic constraints. Computational Statistics and Data Analysis 55, 1715-1725. – reference: Cuesta-Albertos, J. A., Gordaliza, A. and Matrán, C. (1997). Trimmed k-means: An attempt to robustify quantizers. The Annals of Statistics 25, 553-576. – reference: Banfield, J. D. and Raftery, A. E. (1993). Model-based Gaussian and non-Gaussian clustering. Biometrics 49, 803-821. – reference: Flury, B. N. and Gautschi, W. (1986). An algorithm for simultaneous orthogonal transformation of several positive definite matrices to nearly diagonal form. SIAM Journal on Scientific and Statistical Computing 7, 169-184. – reference: Di Zio, M., Guarnera, U. and Rocci, R. (2007). A mixture of mixture models for a classification problem: the unity measure error. Computational Statistics and Data Analysis 51, 2573-2585. – reference: Hartigan, J. A. (1985). Statistical theory in clustering. Journal of Classification 2, 63-76. – reference: García-Escudero, L. A. and Gordaliza, A. (1999). Robustness properties of k means and trimmed k means. Journal of the American Statistical Association 94, 956-969. – reference: Hurley, C. (2004). Clustering visualizations of multivariate data. Journal of Computational and Graphical Statistics 13, 788-806. – reference: Meng, X.-L. and Rubin, D. B. (1993). Maximum likelihood estimation via the ECM algorithm: a general framework. Biometrika 80, 267-278. – reference: McNicholas, P. D., Murphy, T. B., McDaid, A. F. and Frost, D. (2010). Serial and parallel implementations of model-based clustering via parsimonious Gaussian mixture models. Computational Statistics and Data Analysis 54, 711-723. – reference: Ritter, G. (2015). Robust Cluster Analysis and Variable Selection. Vol. 137 of Chapman & Hall/CRC Monographs on Statistics & Applied Probability. CRC Press: Boca Raton, FL. – reference: Hawkins, D. (2013). Identification of Outliers. Monographs on Statistics and Applied Probability. Springer, The Netherlands. – reference: Gallegos, M. T. and Ritter, G. (2005). A robust method for cluster analysis. The Annals of Statistics 33, 347-380. – reference: Coretto, P. and Hennig, C. (2011). Maximum likelihood estimation of heterogeneous mixtures of Gaussian and uniform distributions. Journal of Statistical Planning and Inference 141, 462-473. – reference: Ruwet, C., García-Escudero, L. A., Gordaliza, A. and Mayo-Iscar, A. (2012). The influence function of the tclust robust clustering procedure. Advances in Data Analysis and Classification 6, 107-130. – reference: Böhning, D. (2000). Computer-assisted analysis of mixtures and applications: meta-analysis, disease mapping and others. Vol. 81 of Monographs on Statistics and Applied Probability. Chapman & Hall/CRC, London, UK. – reference: Schwarz, G. (1978). Estimating the dimension of a model. The Annals of Statistics 6, 461-464. – reference: Stephens, M. (2000). Dealing with label switching in mixture models. Journal of the Royal Statistical Society. Series B: Statistical Methodology 62, 795-809. – reference: Ruwet, C., García-Escudero, L. A., Gordaliza, A. and Mayo-Iscar, A. (2013). On the breakdown behavior of the tclust clustering procedure. Test 22, 466-487. – reference: Gerogiannis, D., Nikou, C. and Likas, A. (2009). The mixtures of Student's t-distributions as a robust framework for rigid registration. Image and Vision Computing 27, 1285-1294. – reference: Aitken, A. (1926). A series formula for the roots of algebraic and transcendental equations. Proceedings of the Royal Society of Edinburgh. 45 14-22. – reference: Bagnato, L. and Punzo, A. (2013). Finite mixtures of unimodal beta and gamma densities and the k-bumps algorithm. Computational Statistics 28, 1571-1597. – reference: Teicher, H. (1963). Identifiability of finite mixtures. Annals of Mathematical Statistics 34, 1265-1269. – reference: Fraley, C. and Raftery, A. E. (1998). How many clusters? Which clustering method? Answers via model-based cluster analysis. Computer Journal 41, 578-588. – reference: Crawford, S. L. (1994). An application of the laplace method to finite mixture distributions. Journal of the American Statistical Association 89, 259-267. – reference: McLachlan, G. J. and Basford, K. E. (1988). Mixture Models: Inference and Applications to Clustering. Marcel Dekker, New York, NY. – reference: Peel, D. and McLachlan, G. J. (2000). Robust mixture modelling using the t distribution. Statistics and Computing 10, 339-348. – reference: Andrews, J. L. and McNicholas, P. D. (2012). Model-based clustering, classification, and discriminant analysis with the multivariate t-distribution: the tEIGEN family. Statistics and Computing 22, 1021-1029. – reference: Bai, X., Yao, W. and Boyer, J. E. (2012). Robust fitting of mixture regression models. Computational Statistics and Data Analysis 56, 2347-2359. – reference: Yao, W. (2012). Model based labeling for mixture models. Statistics and Computing 22, 337-347. – reference: García-Escudero, L. A., Gordaliza, A., Matrán, C. and Mayo-Iscar, A. (2008). A general trimming approach to robust cluster analysis. The Annals of Statistics 36, 1324-1345. – reference: Karlis, D. and Xekalaki, E. (2003). Choosing initial values for the EM algorithm for finite mixtures. Computational Statistics and Data Analysis 41, 577-590. – reference: Markatou, M. (2000). Mixture models, robustness, and the weighted likelihood methodology. Biometrics 56, 483-486. – reference: Yao, W., Wei, Y. and Yu, C. (2014). Robust mixture regression using the t-distribution. Computational Statistics and Data Analysis 71, 116-127. – reference: Yakowitz, S. J. and Spragins, J. D. (1968). On the identifiability of finite mixtures. The Annals of Mathematical Statistics 39, 209-214. – reference: Gallegos, M. T. and Ritter, G. (2009). Trimmed ML estimation of contaminated mixtures. Sankhyā: The Indian Journal of Statistics, Series A 71, 164-220. – reference: McNicholas, P. D. (2016). Mixture Model-Based Classification. Chapman & Hall/CRC Press, Boca Raton, FL. – reference: Becker, C. and Gather, U. (1999). The masking breakdown point of multivariate outlier identification rules. Journal of the American Statistical Association 94, 947-955. – reference: Hennig, C. (2002). Fixed point clusters for linear regression: computation and comparison. Journal of Classification 19, 249-276. – reference: Byers, S. and Raftery, A. E. (1998). Nearest-neighbor clutter removal for estimating features in spatial point processes. Journal of the American Statistical Association 93, 577-584. – reference: Campbell, N. A. and Mahon, R. J. (1974). A multivariate study of variation in two species of rock crab of genus Leptograpsus. Australian Journal of Zoology 22, 417-425. – reference: Campbell, N. A. (1984). Mixture models and atypical values. Mathematical Geology 16, 465-477. – reference: Li, J. (2005). Clustering based on a multi-layer mixture model. Journal of Computational and Graphical Statistics 14, 547-568. – reference: Holzmann, H., Munk, A. and Gneiting, T. (2006). Identifiability of finite mixtures of elliptical distributions. Scandinavian Journal of Statistics 33, 753-763. – reference: Lo, Y. (2005). Likelihood ratio tests of the number of components in a normal mixture with unequal variances. Statistics and Probability Letters 71, 225-235. – reference: Aggarwal, C. C. (2013). Outlier Analysis. Springer, New York, NY. – reference: McNicholas, P. D. (2010). Model-based classification using latent Gaussian mixture models. Journal of Statistical Planning and Inference 140, 1175-1181. – reference: Ingrassia, S. (2004). A likelihood-based constrained algorithm for multivariate normal mixture models. Statistical Methods and Applications 13, 151-166. – reference: García-Escudero, L. A., Gordaliza, A. and Matrán, C. (2003). Trimming tools in exploratory data analysis. Journal of Computational and Graphical Statistics 12, 434-449. – reference: Böhning, D., Dietz, E., Schaub, R., Schlattmann, P. and Lindsay, B. (1994). The distribution of the likelihood ratio for mixtures of densities from the one-parameter exponential family. Annals of the Institute of Statistical Mathematics 46, 373-388. – reference: Bock, H. H. (2002). Clustering methods: from classical models to new approaches. Statistics in Transition 5, 725-758. – reference: De Veaux, R. D. and Krieger, A. M. (1990). Robust estimation of a normal mixture. Statistics and Probability Letters 10, 1-7. – reference: Hastie, T. and Tibshirani, R. (1996). Discriminant analysis by Gaussian mixtures. Journal of the Royal Statistical Society: Series B 58, 155-176. – reference: Celeux, G., Hurn, M. and Robert, C. P. (2000). Computational and inferential difficulties with mixture posterior distributions. Journal of the American Statistical Association 95, 957-970. – reference: Lo, Y., Mendell, N. R. and Rubin, D. B. (2001). Testing the number of components in a normal mixture. Biometrika 88, 767-778. – reference: Punzo, A., Browne, R. P. and McNicholas, P. D. (2016). Hypothesis testing for mixture model selection. Journal of Statistical Computation and Simulation. 86, 2797-2818 – reference: Little, R. J. A. (1988). Robust estimation of the mean and covariance matrix from data with missing values. Applied Statistics 37, 23-38. – reference: Biernacki, C. and Chrétien, S. (2003). Degeneracy in the maximum likelihood estimation of univariate Gaussian mixtures with EM. Statistics and Probability Letters 61, 373-382. – reference: Davies, L. and Gather, U. (1993). The identification of multiple outliers. Journal of the American Statistical Association 88, 782-792. – reference: McLachlan, G. J. and Peel, D. (2000). Finite Mixture Models. John Wiley & Sons, New York, NY. – reference: Berkane, M. and Bentler, P. M. (1988). Estimation of contamination parameters and identification of outliers in multivariate data. Sociological Methods and Research 17, 55-64. – reference: Verdinelli, I. and Wasserman, L. (1991). Bayesian analysis of outlier problems using the Gibbs sampler. Statistics and Computing 1, 105-117. – reference: Browne, R. P. and McNicholas, P. D. (2014). Estimating common principal components in high dimensions. Advances in Data Analysis and Classification 8, 217-226. – reference: Hathaway, R. J. (1986). A constrained EM algorithm for univariate normal mixtures. Journal of Statistical Computation and Simulation 23, 211-230. – reference: Ingrassia, S. and Rocci, R. (2007). Constrained monotone em algorithms for finite mixture of multivariate Gaussians. Computational Statistics and Data Analysis 51, 5339-5351. – reference: Barnett, V. and Lewis, T. (1994). Outliers in Statistical Data. Wiley Series in Probability & Statistics. Chichester, UK: John Wiley & Sons. – reference: Hennig, C. (2004). Breakdown points for maximum likelihood estimators of location-scale mixtures. The Annals of Statistics 32, 1313-1340. – reference: Hunter, D. R. and Lange, K. (2000). Rejoinder to discussion of "optimization transfer using surrogate objective functions. Journal of Computational and Graphical Statistics 9, 52-59. – reference: Biernacki, C., Celeux, G. and Govaert, G. (2003). Choosing starting values for the EM algorithm for getting the highest likelihood in multivariate Gaussian mixture models. Computational Statistics and Data Analysis 41, 561-575. – reference: Celeux, G. and Govaert, G. (1995). Gaussian parsimonious clustering models. Pattern Recognition 28, 781-793. – volume: 16 start-page: 465 year: 1984 end-page: 477 article-title: Mixture models and atypical values publication-title: Mathematical Geology – volume: 51 start-page: 5339 year: 2007 end-page: 5351 article-title: Constrained monotone em algorithms for finite mixture of multivariate Gaussians publication-title: Computational Statistics and Data Analysis – volume: 28 start-page: 781 year: 1995 end-page: 793 article-title: Gaussian parsimonious clustering models publication-title: Pattern Recognition – volume: 37 start-page: 23 year: 1988 end-page: 38 article-title: Robust estimation of the mean and covariance matrix from data with missing values publication-title: Applied Statistics – volume: 93 start-page: 577 year: 1998 end-page: 584 article-title: Nearest‐neighbor clutter removal for estimating features in spatial point processes publication-title: Journal of the American Statistical Association – volume: 8 start-page: 217 year: 2014 end-page: 226 article-title: Estimating common principal components in high dimensions publication-title: Advances in Data Analysis and Classification – volume: 25 start-page: 111 year: 1995 end-page: 164 article-title: Bayesian model selection in social research publication-title: Sociological Methodology – volume: 28 start-page: 1571 year: 2013 end-page: 1597 article-title: Finite mixtures of unimodal beta and gamma densities and the ‐bumps algorithm publication-title: Computational Statistics – volume: 45 start-page: 14 year: 1926 end-page: 22 article-title: A series formula for the roots of algebraic and transcendental equations publication-title: Proceedings of the Royal Society of Edinburgh – year: 1994 – volume: 10 start-page: 339 year: 2000 end-page: 348 article-title: Robust mixture modelling using the distribution publication-title: Statistics and Computing – year: 1998 – volume: 56 start-page: 483 year: 2000 end-page: 486 article-title: Mixture models, robustness, and the weighted likelihood methodology publication-title: Biometrics – volume: 1 start-page: 105 year: 1991 end-page: 117 article-title: Bayesian analysis of outlier problems using the Gibbs sampler publication-title: Statistics and Computing – volume: 80 start-page: 267 year: 1993 end-page: 278 article-title: Maximum likelihood estimation via the ECM algorithm: a general framework publication-title: Biometrika – volume: 22 start-page: 417 year: 1974 end-page: 425 article-title: A multivariate study of variation in two species of rock crab of genus Leptograpsus publication-title: Australian Journal of Zoology – volume: 95 start-page: 957 year: 2000 end-page: 970 article-title: Computational and inferential difficulties with mixture posterior distributions publication-title: Journal of the American Statistical Association – volume: 2 start-page: 63 year: 1985 end-page: 76 article-title: Statistical theory in clustering publication-title: Journal of Classification – volume: 56 start-page: 2347 year: 2012 end-page: 2359 article-title: Robust fitting of mixture regression models publication-title: Computational Statistics and Data Analysis – volume: 25 start-page: 553 year: 1997 end-page: 576 article-title: Trimmed ‐means: An attempt to robustify quantizers publication-title: The Annals of Statistics – volume: 62 start-page: 795 year: 2000 end-page: 809 article-title: Dealing with label switching in mixture models publication-title: Journal of the Royal Statistical Society. Series B: Statistical Methodology – year: 1965 – volume: 88 start-page: 767 year: 2001 end-page: 778 article-title: Testing the number of components in a normal mixture publication-title: Biometrika – year: 2008 – volume: 13 start-page: 151 year: 2004 end-page: 166 article-title: A likelihood‐based constrained algorithm for multivariate normal mixture models publication-title: Statistical Methods and Applications – year: 2004 – volume: 34 start-page: 814 year: 2012 end-page: 817 article-title: Model‐based learning using a mixture of mixtures of Gaussian and uniform distributions publication-title: IEEE Transactions on Pattern Analysis and Machine Intelligence – volume: 41 start-page: 577 year: 2003 end-page: 590 article-title: Choosing initial values for the EM algorithm for finite mixtures publication-title: Computational Statistics and Data Analysis – volume: 49 start-page: 803 year: 1993 end-page: 821 article-title: Model‐based Gaussian and non‐Gaussian clustering publication-title: Biometrics – volume: 51 start-page: 2573 year: 2007 end-page: 2585 article-title: A mixture of mixture models for a classification problem: the unity measure error publication-title: Computational Statistics and Data Analysis – start-page: 448 year: 1960 end-page: 485 – volume: 22 start-page: 1021 year: 2012 end-page: 1029 article-title: Model‐based clustering, classification, and discriminant analysis with the multivariate ‐distribution: the EIGEN family publication-title: Statistics and Computing – volume: 27 start-page: 1285 year: 2009 end-page: 1294 article-title: The mixtures of Student's t‐distributions as a robust framework for rigid registration publication-title: Image and Vision Computing – volume: 86 start-page: 2797 year: 2016 end-page: 2818 article-title: Hypothesis testing for mixture model selection publication-title: Journal of Statistical Computation and Simulation – volume: 23 start-page: 211 year: 1986 end-page: 230 article-title: A constrained EM algorithm for univariate normal mixtures publication-title: Journal of Statistical Computation and Simulation – volume: 39 start-page: 1 year: 1977 end-page: 38 article-title: Maximum likelihood from incomplete data via the EM algorithm publication-title: Journal of the Royal Statistical Society: Series B – volume: 18 start-page: 233 year: 2008 end-page: 240 article-title: A likelihood ratio test of a homoscedastic normal mixture against a heteroscedastic normal mixture publication-title: Statistics and Computing – year: 2015 – volume: 5 start-page: 725 year: 2002 end-page: 758 article-title: Clustering methods: from classical models to new approaches publication-title: Statistics in Transition – volume: 10 start-page: 1 year: 1990 end-page: 7 article-title: Robust estimation of a normal mixture publication-title: Statistics and Probability Letters – volume: 71 start-page: 225 year: 2005 end-page: 235 article-title: Likelihood ratio tests of the number of components in a normal mixture with unequal variances publication-title: Statistics and Probability Letters – volume: 12 start-page: 434 year: 2003 end-page: 449 article-title: Trimming tools in exploratory data analysis publication-title: Journal of Computational and Graphical Statistics – volume: 94 start-page: 947 year: 1999 end-page: 955 article-title: The masking breakdown point of multivariate outlier identification rules publication-title: Journal of the American Statistical Association – volume: 13 start-page: 788 year: 2004 end-page: 806 article-title: Clustering visualizations of multivariate data publication-title: Journal of Computational and Graphical Statistics – volume: 17 start-page: 55 year: 1988 end-page: 64 article-title: Estimation of contamination parameters and identification of outliers in multivariate data publication-title: Sociological Methods and Research – volume: 71 start-page: 164 year: 2009 end-page: 220 article-title: Trimmed ML estimation of contaminated mixtures publication-title: Sankhyā: The Indian Journal of Statistics, Series A – volume: 71 start-page: 116 year: 2014 end-page: 127 article-title: Robust mixture regression using the ‐distribution publication-title: Computational Statistics and Data Analysis – volume: 41 start-page: 561 year: 2003 end-page: 575 article-title: Choosing starting values for the EM algorithm for getting the highest likelihood in multivariate Gaussian mixture models publication-title: Computational Statistics and Data Analysis – volume: 141 start-page: 462 year: 2011 end-page: 473 article-title: Maximum likelihood estimation of heterogeneous mixtures of Gaussian and uniform distributions publication-title: Journal of Statistical Planning and Inference – volume: 58 start-page: 155 year: 1996 end-page: 176 article-title: Discriminant analysis by Gaussian mixtures publication-title: Journal of the Royal Statistical Society: Series B – year: 2007 – start-page: 658 year: 1998 end-page: 666 – year: 2000 – volume: 36 start-page: 1324 year: 2008 end-page: 1345 article-title: A general trimming approach to robust cluster analysis publication-title: The Annals of Statistics – volume: 33 start-page: 347 year: 2005 end-page: 380 article-title: A robust method for cluster analysis publication-title: The Annals of Statistics – year: 2016 – volume: 4 start-page: 89 year: 2010 end-page: 109 article-title: A review of robust clustering methods publication-title: Advances in Data Analysis and Classification – volume: 6 start-page: 107 year: 2012 end-page: 130 article-title: The influence function of the tclust robust clustering procedure publication-title: Advances in Data Analysis and Classification – volume: 6 start-page: 461 year: 1978 end-page: 464 article-title: Estimating the dimension of a model publication-title: The Annals of Statistics – year: 2012 – volume: 89 start-page: 259 year: 1994 end-page: 267 article-title: An application of the laplace method to finite mixture distributions publication-title: Journal of the American Statistical Association – volume: 22 start-page: 325 year: 1980 end-page: 331 article-title: Mixture models, outliers, and the EM algorithm publication-title: Technometrics – volume: 7 start-page: 169 year: 1986 end-page: 184 article-title: An algorithm for simultaneous orthogonal transformation of several positive definite matrices to nearly diagonal form publication-title: SIAM Journal on Scientific and Statistical Computing – volume: 55 start-page: 177 year: 2002 end-page: 182 article-title: A note on the maximum deviation of the scale‐contaminated normal to the best normal distribution publication-title: Metrika – volume: 33 start-page: 753 year: 2006 end-page: 763 article-title: Identifiability of finite mixtures of elliptical distributions publication-title: Scandinavian Journal of Statistics – volume: 34 start-page: 1265 year: 1963 end-page: 1269 article-title: Identifiability of finite mixtures publication-title: Annals of Mathematical Statistics – volume: 55 start-page: 1715 year: 2011 end-page: 1725 article-title: Degeneracy of the EM algorithm for the mle of multivariate Gaussian mixtures and dynamic constraints publication-title: Computational Statistics and Data Analysis – year: 1988 – volume: 140 start-page: 1175 year: 2010 end-page: 1181 article-title: Model‐based classification using latent Gaussian mixture models publication-title: Journal of Statistical Planning and Inference – volume: 61 start-page: 373 year: 2003 end-page: 382 article-title: Degeneracy in the maximum likelihood estimation of univariate Gaussian mixtures with EM publication-title: Statistics and Probability Letters – volume: 39 start-page: 209 year: 1968 end-page: 214 article-title: On the identifiability of finite mixtures publication-title: The Annals of Mathematical Statistics – volume: 19 start-page: 249 year: 2002 end-page: 276 article-title: Fixed point clusters for linear regression: computation and comparison publication-title: Journal of Classification – volume: 88 start-page: 782 year: 1993 end-page: 792 article-title: The identification of multiple outliers publication-title: Journal of the American Statistical Association – volume: 9 start-page: 52 year: 2000 end-page: 59 article-title: Rejoinder to discussion of “optimization transfer using surrogate objective functions publication-title: Journal of Computational and Graphical Statistics – volume: 54 start-page: 711 year: 2010 end-page: 723 article-title: Serial and parallel implementations of model‐based clustering via parsimonious Gaussian mixture models publication-title: Computational Statistics and Data Analysis – volume: 22 start-page: 337 year: 2012 end-page: 347 article-title: Model based labeling for mixture models publication-title: Statistics and Computing – volume: 22 start-page: 466 year: 2013 end-page: 487 article-title: On the breakdown behavior of the tclust clustering procedure publication-title: Test – volume: 46 start-page: 373 year: 1994 end-page: 388 article-title: The distribution of the likelihood ratio for mixtures of densities from the one‐parameter exponential family publication-title: Annals of the Institute of Statistical Mathematics – volume: 32 start-page: 1313 year: 2004 end-page: 1340 article-title: Breakdown points for maximum likelihood estimators of location‐scale mixtures publication-title: The Annals of Statistics – volume: 41 start-page: 578 year: 1998 end-page: 588 article-title: How many clusters? Which clustering method? Answers via model‐based cluster analysis publication-title: Computer Journal – volume: 14 start-page: 547 year: 2005 end-page: 568 article-title: Clustering based on a multi‐layer mixture model publication-title: Journal of Computational and Graphical Statistics – year: 2013 – volume: 94 start-page: 956 year: 1999 end-page: 969 article-title: Robustness properties of means and trimmed means publication-title: Journal of the American Statistical Association – ident: e_1_2_11_35_1 doi: 10.1016/0167-7152(90)90104-F – ident: e_1_2_11_29_1 doi: 10.1080/01621459.2000.10474285 – ident: e_1_2_11_41_1 – ident: e_1_2_11_74_1 doi: 10.1002/0471721182 – ident: e_1_2_11_24_1 – ident: e_1_2_11_67_1 doi: 10.1016/j.spl.2004.11.007 – ident: e_1_2_11_88_1 doi: 10.1111/1467-9868.00265 – ident: e_1_2_11_5_1 doi: 10.1007/s11222-011-9272-x – volume: 94 start-page: 956 year: 1999 ident: e_1_2_11_45_1 article-title: Robustness properties of k means and trimmed k means publication-title: Journal of the American Statistical Association – ident: e_1_2_11_39_1 – ident: e_1_2_11_76_1 doi: 10.1201/9781315373577 – ident: e_1_2_11_80_1 doi: 10.1080/00949655.2015.1131282 – ident: e_1_2_11_27_1 doi: 10.1071/ZO9740417 – ident: e_1_2_11_7_1 doi: 10.1007/s00180-012-0367-4 – ident: e_1_2_11_52_1 doi: 10.1080/00949658608810872 – ident: e_1_2_11_54_1 doi: 10.1007/s00357-001-0045-7 – volume-title: Identification of Outliers. Monographs on Statistics and Applied Probability year: 2013 ident: e_1_2_11_53_1 – ident: e_1_2_11_55_1 doi: 10.1214/009053604000000571 – ident: e_1_2_11_81_1 – ident: e_1_2_11_37_1 doi: 10.1016/j.csda.2006.01.001 – ident: e_1_2_11_61_1 doi: 10.1016/j.csda.2006.10.011 – ident: e_1_2_11_48_1 doi: 10.1007/s11634-010-0064-5 – ident: e_1_2_11_8_1 doi: 10.1016/j.csda.2012.01.016 – ident: e_1_2_11_86_1 doi: 10.1007/s11749-012-0312-4 – ident: e_1_2_11_75_1 doi: 10.1016/j.jspi.2009.11.006 – volume: 5 start-page: 725 year: 2002 ident: e_1_2_11_17_1 article-title: Clustering methods: from classical models to new approaches publication-title: Statistics in Transition – ident: e_1_2_11_28_1 doi: 10.1016/0031-3203(94)00125-6 – ident: e_1_2_11_6_1 – ident: e_1_2_11_83_1 doi: 10.2307/271063 – ident: e_1_2_11_65_1 doi: 10.1198/106186005X59586 – ident: e_1_2_11_32_1 doi: 10.1080/01621459.1994.10476467 – volume: 39 start-page: 1 year: 1977 ident: e_1_2_11_36_1 article-title: Maximum likelihood from incomplete data via the EM algorithm publication-title: Journal of the Royal Statistical Society: Series B doi: 10.1111/j.2517-6161.1977.tb01600.x – ident: e_1_2_11_40_1 doi: 10.1093/comjnl/41.8.578 – ident: e_1_2_11_20_1 doi: 10.1007/s001840100138 – ident: e_1_2_11_69_1 doi: 10.1093/biomet/88.3.767 – volume-title: Vol. 382 of Wiley Series in Probability and Statistics year: 2007 ident: e_1_2_11_71_1 – ident: e_1_2_11_91_1 doi: 10.1007/BF01889985 – ident: e_1_2_11_30_1 doi: 10.1016/j.jspi.2010.06.024 – ident: e_1_2_11_58_1 doi: 10.1080/10618600.2000.10474865 – ident: e_1_2_11_57_1 doi: 10.1111/j.1467-9469.2006.00505.x – ident: e_1_2_11_62_1 doi: 10.1016/j.csda.2010.10.026 – ident: e_1_2_11_68_1 doi: 10.1007/s11222-008-9052-4 – ident: e_1_2_11_79_1 doi: 10.1023/A:1008981510081 – ident: e_1_2_11_22_1 – ident: e_1_2_11_2_1 doi: 10.1007/978-1-4614-6396-2 – ident: e_1_2_11_13_1 – ident: e_1_2_11_19_1 doi: 10.1007/BF01720593 – ident: e_1_2_11_43_1 doi: 10.1214/009053604000000940 – ident: e_1_2_11_89_1 doi: 10.1214/aoms/1177703862 – volume-title: Computer‐assisted analysis of mixtures and applications: meta‐analysis, disease mapping and others. Vol. 81 of Monographs on Statistics and Applied Probability year: 2000 ident: e_1_2_11_18_1 doi: 10.1080/00401706.2000.10485740 – ident: e_1_2_11_26_1 doi: 10.1007/BF01886327 – ident: e_1_2_11_9_1 doi: 10.2307/2532201 – ident: e_1_2_11_82_1 – ident: e_1_2_11_92_1 doi: 10.21236/AD0620026 – ident: e_1_2_11_70_1 doi: 10.1111/j.0006-341X.2000.00483.x – ident: e_1_2_11_78_1 doi: 10.1093/biomet/80.2.267 – ident: e_1_2_11_66_1 doi: 10.2307/2347491 – volume-title: Robust Cluster Analysis and Variable Selection. Vol. 137 of Chapman & Hall/CRC Monographs on Statistics & Applied Probability year: 2015 ident: e_1_2_11_84_1 – start-page: 448 volume-title: Contributions to Probability and Statistics: Essays in Honor of Harold Hotelling. Stanford Studies in Mathematics and Statistics year: 1960 ident: e_1_2_11_90_1 – ident: e_1_2_11_4_1 doi: 10.1080/00401706.1980.10486163 – ident: e_1_2_11_60_1 doi: 10.1007/s10260-004-0092-4 – ident: e_1_2_11_47_1 doi: 10.1214/07-AOS515 – ident: e_1_2_11_3_1 doi: 10.1017/S0370164600024871 – ident: e_1_2_11_77_1 doi: 10.1016/j.csda.2009.02.011 – ident: e_1_2_11_25_1 doi: 10.1080/01621459.1998.10473711 – ident: e_1_2_11_33_1 doi: 10.1214/aos/1031833664 – volume-title: Mixture Models: Inference and Applications to Clustering year: 1988 ident: e_1_2_11_72_1 – ident: e_1_2_11_94_1 doi: 10.1007/s11222-010-9226-8 – ident: e_1_2_11_42_1 – ident: e_1_2_11_16_1 doi: 10.1016/S0167-7152(02)00396-6 – ident: e_1_2_11_46_1 doi: 10.1198/1061860031806 – ident: e_1_2_11_15_1 – ident: e_1_2_11_11_1 doi: 10.1080/01621459.1999.10474199 – ident: e_1_2_11_14_1 doi: 10.1016/S0167-9473(02)00163-9 – ident: e_1_2_11_21_1 doi: 10.1007/s11634-013-0139-1 – ident: e_1_2_11_31_1 – ident: e_1_2_11_34_1 doi: 10.1080/01621459.1993.10476339 – ident: e_1_2_11_12_1 doi: 10.1177/0049124188017001003 – ident: e_1_2_11_23_1 doi: 10.1109/TPAMI.2011.199 – ident: e_1_2_11_38_1 doi: 10.1137/0907013 – ident: e_1_2_11_63_1 doi: 10.1016/S0167-9473(02)00177-9 – ident: e_1_2_11_87_1 doi: 10.1214/aos/1176344136 – ident: e_1_2_11_95_1 doi: 10.1016/j.csda.2013.07.019 – volume-title: Outliers in Statistical Data year: 1994 ident: e_1_2_11_10_1 – ident: e_1_2_11_59_1 doi: 10.1198/106186004X12425 – ident: e_1_2_11_64_1 – start-page: 658 volume-title: Advances in Pattern Recognition. Vol. 1451 of Lecture Notes in Computer Science year: 1998 ident: e_1_2_11_73_1 – ident: e_1_2_11_56_1 – ident: e_1_2_11_49_1 doi: 10.1016/j.imavis.2008.11.013 – volume: 71 start-page: 164 year: 2009 ident: e_1_2_11_44_1 article-title: Trimmed ML estimation of contaminated mixtures publication-title: Sankhyā: The Indian Journal of Statistics, Series A – volume: 58 start-page: 155 year: 1996 ident: e_1_2_11_51_1 article-title: Discriminant analysis by Gaussian mixtures publication-title: Journal of the Royal Statistical Society: Series B doi: 10.1111/j.2517-6161.1996.tb02073.x – ident: e_1_2_11_50_1 doi: 10.1007/BF01908064 – ident: e_1_2_11_93_1 doi: 10.1214/aoms/1177698520 – ident: e_1_2_11_85_1 doi: 10.1007/s11634-012-0107-1
SSID	ssj0009042
Score	2.4706352
Snippet	A mixture of multivariate contaminated normal distributions is developed for model‐based clustering. In addition to the parameters of the classical normal... A mixture of multivariate contaminated normal distributions is developed for model-based clustering. In addition to the parameters of the classical normal...
SourceID	proquest pubmed crossref wiley istex
SourceType	Aggregation Database Index Database Enrichment Source Publisher
StartPage	1506
SubjectTerms	Algorithms Cluster Analysis Contaminated normal distribution Contamination EM algorithm Mixture models Model-based clustering Models, Statistical Normal Distribution
Title	Parsimonious mixtures of multivariate contaminated normal distributions
URI	https://api.istex.fr/ark:/67375/WNG-KJH5QNT0-T/fulltext.pdf https://onlinelibrary.wiley.com/doi/abs/10.1002%2Fbimj.201500144 https://www.ncbi.nlm.nih.gov/pubmed/27510372 https://www.proquest.com/docview/1834787788 https://www.proquest.com/docview/1835536426 https://www.proquest.com/docview/1846397553
Volume	58
WOSCitedRecordID	wos000387148100014&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText	1
inHoldings	1
isFullTextHit
isPrint
journalDatabaseRights	– providerCode: PRVWIB databaseName: Wiley Online Library Full Collection 2020 customDbUrl: eissn: 1521-4036 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0009042 issn: 0323-3847 databaseCode: DRFUL dateStart: 19980101 isFulltext: true titleUrlDefault: https://onlinelibrary.wiley.com providerName: Wiley-Blackwell
link	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3db9MwED9tLUi8wMbXMropSAierKVJHDuP46Mb3agG6qBvluM4UlmXoaaruv-euyRNqbQNIZ4iJacoOd_H7-zzzwBvYp7QHpmEGUwvjDIEk12uGaY-Y8IYL-V8x_dTMRjI0Sg--2MXf8UP0Uy4kWeU8ZocXCfFwYo0NBlf_qTWLE4oP9yEto_Gy1vQ_vitd366It71wmolwQ9YgKF4Sdzo-Qfrb1hLTG3S8eI21LkOYsss1Hvy_9-_BY9rBOoeViazDRs2fwoPqzMpb57B0RmWujiAOTXHupfjBS0xFO5V5pa9h3OsrRGeutTirqmNBhGrmxPwnbgpkfDW52cVz-G892n44ZjVpy0wgygoYGlqjCHye4RUwqAzWo61SGZtYtDpdZYg8BAmRQQkUuNHJgs4GgA3cayJdE0GL6CVX-V2B1yLqCaMEuHFEs0AY6KRWns6kV4WishaB9hS1crUVOR0IsZEVSTKviLlqEY5Drxr5H9VJBx3Sr4tR64R09MLal0TXP0YHKmT_jH_Ohh6auhAZzm0qvbaQmF4I64iIaUDr5vH6G-0iKJzi3onGc4DrNqi-2RCWi9FOQdeVmbTfJAviMNQ-KiD0jr-8kPq_ecv_a7oBrv_KP8KHuHNqNo22YHWbHpt9-CBmc_GxXQfNsVI7te-8hsF1RKJ
linkProvider	Wiley-Blackwell
linkToHtml	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1LT9wwEB6VXRBcKI_ShmcqofZkkU3iODlCy7LAElG0tNwsx3Gk5ZFFuxTRf89Mkg1aCYqQOOWQURSP5_GNPf4MsB3xhM7IJExjemGUIVjY4oph6tPaj_BRrHf87oo4Di8uotOqm5DOwpT8EPWCG3lGEa_JwWlBeueJNTTp31xSbxYnmO9PQdNHW0Ijb_48a593n5h3Hb_cSnA95mEsHjM3Ou7O5BcmMlOTlPzwHOycRLFFGmp_fIcBLMB8hUHt3dJoFuGDyZdgpryV8t8yHJxisYtTmFN7rH3Tf6BNhpE9yOyi-_Aeq2sEqDY1uStqpEHMaucEfa_tlGh4qxu0Rp_gvL3f-9Fh1X0LTCMO8liaaq2J_h5BldDojoZjNZIZk2h0e5UlCD2EThEDiVS7gc48jibAdRQpol0LvRVo5IPcfAHbIK7xg0Q4UYiGgFFRh0o5KgmdzBeBMRawsa6lrsjI6U6Ma1nSKLuSlCNr5VjwvZa_LWk4XpT8VkxdLaaGV9S8Jrj8Ex_I46MO_xX3HNmzYH08t7Ly25HEAEdsRSIMLfhav0aPo20UlRvUO8lw7mHdFvxPxqcdU5Sz4HNpN_UPuYJYDIWLOijM45UByb3Dk6OWaHmrb5TfgtlO76Qru4fx8RrMoUBQHqJch8bd8K_ZgGl9f9cfDTcrl3kE_uEVkQ
linkToPdf	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1LT9wwEB7R3RZxAUp5BCgNUlVOFtkkjpMjr-W1jRa0PG6W4zjS8ghoFxD8e2aSbNBKbVElTjl4FMXjGc_nzPgbgJ8RT-iOTMI0hhdGEYKFLa4Yhj6t_Qgfxf-O846I4_DyMupW1YR0F6bkh6h_uJFnFPs1Obi5T7PNN9bQpH97RbVZnGC-_wmaPnWSaUBz97R91nlj3nX8MpXgeszDvXjE3Oi4m-NvGItMTVLy859g5ziKLcJQe-YDJjAL0xUGtbdKo_kKEyafgy9lV8qXb7DfxcMuLmFO5bH2bf-ZkgxD-y6zi-rDJzxdI0C1qchdUSENYlY7J-h7Y6dEw1t10BrOw1l7r7dzwKp-C0wjDvJYmmqtif4eQZXQ6I6G42kkMybR6PYqSxB6CJ0iBhKpdgOdeRxNgOsoUkS7FnoL0MjvcrMEtkFc4weJcKIQDQF3RR0q5agkdDJfBMZYwEa6lroiI6eeGDeypFF2JSlH1sqxYKOWvy9pOP4q-atYulpMDa6peE1weRHvy-OjA34S9xzZs2B1tLay8tuhxA2O2IpEGFqwXg-jx1EaReUG9U4ynHt4bgv-JeNTxhTlLFgs7ab-IFcQi6FwUQeFebwzIbl9-PuoJVre8n_K_4DJ7m5bdg7j4xWYwvGgvEO5Co2HwaP5Dp_100N_OFirPOYVaVEVDA
openUrl	ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Parsimonious+mixtures+of+multivariate+contaminated+normal+distributions&rft.jtitle=Biometrical+journal&rft.au=Punzo%2C+Antonio&rft.au=McNicholas%2C+Paul+D.&rft.date=2016-11-01&rft.issn=0323-3847&rft.eissn=1521-4036&rft.volume=58&rft.issue=6&rft.spage=1506&rft.epage=1537&rft_id=info:doi/10.1002%2Fbimj.201500144&rft.externalDBID=n%2Fa&rft.externalDocID=10_1002_bimj_201500144
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0323-3847&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0323-3847&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0323-3847&client=summon