A compound decision approach to covariance matrix estimation
Covariance matrix estimation is a fundamental statistical task in many applications, but the sample covariance matrix is suboptimal when the sample size is comparable to or less than the number of features. Such high‐dimensional settings are common in modern genomics, where covariance matrix estimat...
Uložené v:
| Vydané v: | Biometrics Ročník 79; číslo 2; s. 1201 - 1212 |
|---|---|
| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
United States
Blackwell Publishing Ltd
01.06.2023
|
| Predmet: | |
| ISSN: | 0006-341X, 1541-0420, 1541-0420 |
| On-line prístup: | Získať plný text |
| Tagy: |
Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
|
| Abstract | Covariance matrix estimation is a fundamental statistical task in many applications, but the sample covariance matrix is suboptimal when the sample size is comparable to or less than the number of features. Such high‐dimensional settings are common in modern genomics, where covariance matrix estimation is frequently employed as a method for inferring gene networks. To achieve estimation accuracy in these settings, existing methods typically either assume that the population covariance matrix has some particular structure, for example, sparsity, or apply shrinkage to better estimate the population eigenvalues. In this paper, we study a new approach to estimating high‐dimensional covariance matrices. We first frame covariance matrix estimation as a compound decision problem. This motivates defining a class of decision rules and using a nonparametric empirical Bayes g‐modeling approach to estimate the optimal rule in the class. Simulation results and gene network inference in an RNA‐seq experiment in mouse show that our approach is comparable to or can outperform a number of state‐of‐the‐art proposals. |
|---|---|
| AbstractList | Covariance matrix estimation is a fundamental statistical task in many applications, but the sample covariance matrix is suboptimal when the sample size is comparable to or less than the number of features. Such high-dimensional settings are common in modern genomics, where covariance matrix estimation is frequently employed as a method for inferring gene networks. To achieve estimation accuracy in these settings, existing methods typically either assume that the population covariance matrix has some particular structure, for example, sparsity, or apply shrinkage to better estimate the population eigenvalues. In this paper, we study a new approach to estimating high-dimensional covariance matrices. We first frame covariance matrix estimation as a compound decision problem. This motivates defining a class of decision rules and using a nonparametric empirical Bayes g-modeling approach to estimate the optimal rule in the class. Simulation results and gene network inference in an RNA-seq experiment in mouse show that our approach is comparable to or can outperform a number of state-of-the-art proposals.Covariance matrix estimation is a fundamental statistical task in many applications, but the sample covariance matrix is suboptimal when the sample size is comparable to or less than the number of features. Such high-dimensional settings are common in modern genomics, where covariance matrix estimation is frequently employed as a method for inferring gene networks. To achieve estimation accuracy in these settings, existing methods typically either assume that the population covariance matrix has some particular structure, for example, sparsity, or apply shrinkage to better estimate the population eigenvalues. In this paper, we study a new approach to estimating high-dimensional covariance matrices. We first frame covariance matrix estimation as a compound decision problem. This motivates defining a class of decision rules and using a nonparametric empirical Bayes g-modeling approach to estimate the optimal rule in the class. Simulation results and gene network inference in an RNA-seq experiment in mouse show that our approach is comparable to or can outperform a number of state-of-the-art proposals. Covariance matrix estimation is a fundamental statistical task in many applications, but the sample covariance matrix is suboptimal when the sample size is comparable to or less than the number of features. Such high‐dimensional settings are common in modern genomics, where covariance matrix estimation is frequently employed as a method for inferring gene networks. To achieve estimation accuracy in these settings, existing methods typically either assume that the population covariance matrix has some particular structure, for example, sparsity, or apply shrinkage to better estimate the population eigenvalues. In this paper, we study a new approach to estimating high‐dimensional covariance matrices. We first frame covariance matrix estimation as a compound decision problem. This motivates defining a class of decision rules and using a nonparametric empirical Bayes g‐modeling approach to estimate the optimal rule in the class. Simulation results and gene network inference in an RNA‐seq experiment in mouse show that our approach is comparable to or can outperform a number of state‐of‐the‐art proposals. Covariance matrix estimation is a fundamental statistical task in many applications, but the sample covariance matrix is suboptimal when the sample size is comparable to or less than the number of features. Such high‐dimensional settings are common in modern genomics, where covariance matrix estimation is frequently employed as a method for inferring gene networks. To achieve estimation accuracy in these settings, existing methods typically either assume that the population covariance matrix has some particular structure, for example, sparsity, or apply shrinkage to better estimate the population eigenvalues. In this paper, we study a new approach to estimating high‐dimensional covariance matrices. We first frame covariance matrix estimation as a compound decision problem. This motivates defining a class of decision rules and using a nonparametric empirical Bayes g‐modeling approach to estimate the optimal rule in the class. Simulation results and gene network inference in an RNA‐seq experiment in mouse show that our approach is comparable to or can outperform a number of state‐of‐the‐art proposals. |
| Author | Xin, Huiqin Zhao, Sihai Dave |
| Author_xml | – sequence: 1 givenname: Huiqin orcidid: 0000-0002-2363-9283 surname: Xin fullname: Xin, Huiqin email: huiqinx2@illinois.edu organization: University of Illinois at Urbana‐Champaign – sequence: 2 givenname: Sihai Dave surname: Zhao fullname: Zhao, Sihai Dave organization: University of Illinois at Urbana‐Champaign |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/35499364$$D View this record in MEDLINE/PubMed |
| BookMark | eNqFkV9LwzAUxYNM3Ka--AGk4IsInUmapin4Mod_BhNfFHwLbXqLGW0zk1bdtzdb54uI5iUJ-d1zc88Zo0FjGkDohOAJ8esy16aekIgLvodGJGYkxIziARphjHkYMfIyRGPnlv6axpgeoGEUszSNOBuhq2mgTL0yXVMEBSjttGmCbLWyJlOvQWv863tmddYoCOqstfozANdqf_TgEdovs8rB8W4_RM-3N0-z-3DxeDefTRehYpTzsBBJATQXLOcMEkwxwZxDDmVEEl5AmpOclWmJc0JLkjIqKOZMlaBAAGNRFB2i817Xf-ut8_1lrZ2CqsoaMJ2TVLBUCEI4_R_lseAspph59OwHujSdbfwgXpAm3kKabHqf7qgur6GQK-uHt2v5baEHcA8oa5yzUEql2609rc10JQmWm5TkJiW5TcmXXPwo-Vb9FSY9_KErWP9Byuv540Nf8wVQxaAz |
| CitedBy_id | crossref_primary_10_1080_24754269_2025_2484979 crossref_primary_10_1177_21582440231174777 |
| Cites_doi | 10.1214/13-STS455 10.1214/aos/1176346059 10.1007/978-3-030-02185-6 10.1214/aos/1051027872 10.1214/08-AOS630 10.1186/1471-2105-9-559 10.2202/1544-6115.1175 10.1214/aoms/1177728066 10.1198/jasa.2009.0101 10.1080/01621459.1978.10480103 10.1016/0024-3795(88)90223-6 10.1214/08-AOS638 10.2139/ssrn.3486378 10.2202/1544-6115.1128 10.1214/19-AOS1817 10.1016/j.jmva.2017.03.001 10.1016/j.csda.2018.01.006 10.1016/j.jeconom.2008.09.017 10.1214/15-AOS1393 10.1109/TSP.2008.929662 10.1109/TIT.2016.2616132 10.1101/368316 10.1007/BF01085007 10.1080/01621459.1995.10476626 10.1525/9780520411586-011 10.1080/01621459.2013.869224 10.1016/S0047-259X(03)00096-4 10.1198/jasa.2011.tm10560 10.1214/ss/1177012274 10.1101/gr.214221.116 10.1080/01621459.2012.725386 10.1186/1471-2105-8-S6-S5 10.1214/12-AOS989 |
| ContentType | Journal Article |
| Copyright | 2022 The Authors. published by Wiley Periodicals LLC on behalf of International Biometric Society. 2022 The Authors. Biometrics published by Wiley Periodicals LLC on behalf of International Biometric Society. 2022. This article is published under http://creativecommons.org/licenses/by-nc-nd/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
| Copyright_xml | – notice: 2022 The Authors. published by Wiley Periodicals LLC on behalf of International Biometric Society. – notice: 2022 The Authors. Biometrics published by Wiley Periodicals LLC on behalf of International Biometric Society. – notice: 2022. This article is published under http://creativecommons.org/licenses/by-nc-nd/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
| DBID | 24P AAYXX CITATION CGR CUY CVF ECM EIF NPM JQ2 7X8 7S9 L.6 |
| DOI | 10.1111/biom.13686 |
| DatabaseName | Wiley-Blackwell Open Access Titles CrossRef Medline MEDLINE MEDLINE (Ovid) MEDLINE MEDLINE PubMed ProQuest Computer Science Collection MEDLINE - Academic AGRICOLA AGRICOLA - Academic |
| DatabaseTitle | CrossRef MEDLINE Medline Complete MEDLINE with Full Text PubMed MEDLINE (Ovid) ProQuest Computer Science Collection MEDLINE - Academic AGRICOLA AGRICOLA - Academic |
| DatabaseTitleList | MEDLINE - Academic MEDLINE AGRICOLA ProQuest Computer Science Collection CrossRef |
| Database_xml | – sequence: 1 dbid: 24P name: Wiley Online Library Open Access url: https://authorservices.wiley.com/open-science/open-access/browse-journals.html sourceTypes: Publisher – sequence: 2 dbid: NPM name: PubMed url: http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed sourceTypes: Index Database – sequence: 3 dbid: 7X8 name: MEDLINE - Academic url: https://search.proquest.com/medline sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Statistics Biology Mathematics |
| EISSN | 1541-0420 |
| EndPage | 1212 |
| ExternalDocumentID | 35499364 10_1111_biom_13686 BIOM13686 |
| Genre | article Journal Article |
| GroupedDBID | --- -~X .3N .4S .DC .GA .GJ .Y3 05W 0R~ 10A 1OC 23N 24P 2AX 2QV 3-9 31~ 33P 36B 3SF 3V. 4.4 44B 50Y 50Z 51W 51X 52M 52N 52O 52P 52S 52T 52U 52W 52X 53G 5GY 5HH 5LA 5RE 5VS 66C 6J9 702 7PT 7X7 8-0 8-1 8-3 8-4 8-5 88E 88I 8AF 8C1 8FE 8FG 8FH 8FI 8FJ 8R4 8R5 8UM 930 A03 A8Z AAESR AAEVG AAHBH AAHHS AANHP AANLZ AAONW AASGY AAUAY AAXRX AAYCA AAZKR AAZSN ABBHK ABCQN ABCUV ABDBF ABDFA ABEJV ABEML ABFAN ABJCF ABJNI ABLJU ABMNT ABPPZ ABPVW ABTAH ABUWG ABXSQ ABXVV ABYWD ACAHQ ACBWZ ACCFJ ACCZN ACFBH ACGFO ACGFS ACGOD ACIWK ACKIV ACMTB ACNCT ACPOU ACPRK ACRPL ACSCC ACTMH ACUHS ACXBN ACXQS ACYXJ ADBBV ADEOM ADIPN ADIZJ ADKYN ADMGS ADNMO ADODI ADOZA ADULT ADVOB ADXAS ADZMN ADZOD AEEZP AEGXH AEIGN AEIMD AELPN AENEX AEQDE AEUPB AEUQT AEUYR AFBPY AFDVO AFEBI AFFTP AFGKR AFKRA AFPWT AFVYC AFWVQ AFZJQ AGTJU AHMBA AIAGR AIBGX AIURR AIWBW AJAOE AJBDE AJXKR ALAGY ALEEW ALIPV ALMA_UNASSIGNED_HOLDINGS ALRMG ALUQN AMBMR AMYDB APXXL ARAPS ARCSS ASPBG AS~ ATUGU AUFTA AVWKF AZBYB AZFZN AZQEC AZVAB BAFTC BBNVY BCRHZ BDRZF BENPR BFHJK BGLVJ BHBCM BHPHI BMNLL BMXJE BNHUX BPHCQ BROTX BRXPI BVXVI BY8 CAG CCPQU COF CS3 D-E D-F DCZOG DPXWK DQDLB DR2 DRFUL DRSTM DSRWC DWQXO DXH EAD EAP EBC EBD EBS ECEWR EDO EJD EMB EMK EMOBN EST ESX F00 F01 F04 F5P FD6 FEDTE FXEWX FYUFA G-S G.N GNUQQ GODZA GS5 H.T H.X HCIFZ HF~ HGD HMCUK HQ6 HVGLF HZI HZ~ IHE IPSME IX1 J0M JAAYA JAC JBMMH JBZCM JENOY JHFFW JKQEH JLEZI JLXEF JMS JPL JSODD JST K48 K6V K7- KOP L6V LATKE LC2 LC3 LEEKS LH4 LITHE LK8 LOXES LP6 LP7 LUTES LW6 LYRES M1P M2P M7P M7S MK4 MRFUL MRSTM MSFUL MSSTM MVM MXFUL MXSTM N04 N05 N9A NF~ NHB NU- O66 O9- OIG OJZSN OWPYF P0- P2P P2W P2X P4D P62 PQQKQ PROAC PSQYO PTHSS Q.N Q11 Q2X QB0 R.K RNS ROL ROX RWL RX1 RXW SA0 SUPJJ SV3 TAE TN5 TUS UAP UB1 UKHRP V8K VQA W8V W99 WBKPD WH7 WIH WIK WOHZO WQJ WRC WYISQ X6Y XBAML XG1 XSW ZGI ZXP ZY4 ZZTAW ~02 ~IA ~KM ~WT AAMMB AAYXX ABGNP ADNBA AEFGJ AEOTA AGXDD AIDQK AIDYY AJNCP CITATION H13 O8X AAWIL ABAWQ ACHJO AGLNM AGORE AGQPQ AHGBF AIHAF AJBYB CGR CUY CVF ECM EIF NPM PHGZM PHGZT PJZUB PPXIY PQGLB ESTFP JQ2 7X8 7S9 L.6 |
| ID | FETCH-LOGICAL-c4266-d87de2b84b64e70201066ebef3176de9b1b4f9f0b12f194282064cfece8e44333 |
| IEDL.DBID | 24P |
| ISICitedReferencesCount | 2 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000799422000001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0006-341X 1541-0420 |
| IngestDate | Thu Oct 02 23:52:19 EDT 2025 Sun Sep 28 08:19:30 EDT 2025 Mon Nov 10 02:54:17 EST 2025 Mon Jul 21 05:51:28 EDT 2025 Sat Nov 29 02:10:10 EST 2025 Tue Nov 18 21:03:44 EST 2025 Wed Jan 22 16:19:37 EST 2025 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 2 |
| Keywords | g-modeling separable decision rule nonparametric maximum likelihood compound decision theory |
| Language | English |
| License | Attribution-NonCommercial-NoDerivs http://creativecommons.org/licenses/by-nc-nd/4.0 2022 The Authors. Biometrics published by Wiley Periodicals LLC on behalf of International Biometric Society. |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c4266-d87de2b84b64e70201066ebef3176de9b1b4f9f0b12f194282064cfece8e44333 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 content type line 23 |
| ORCID | 0000-0002-2363-9283 |
| OpenAccessLink | https://onlinelibrary.wiley.com/doi/abs/10.1111%2Fbiom.13686 |
| PMID | 35499364 |
| PQID | 2827420273 |
| PQPubID | 35366 |
| PageCount | 12 |
| ParticipantIDs | proquest_miscellaneous_2849881162 proquest_miscellaneous_2658645204 proquest_journals_2827420273 pubmed_primary_35499364 crossref_citationtrail_10_1111_biom_13686 crossref_primary_10_1111_biom_13686 wiley_primary_10_1111_biom_13686_BIOM13686 |
| PublicationCentury | 2000 |
| PublicationDate | June 2023 2023-06-01 2023-Jun 20230601 |
| PublicationDateYYYYMMDD | 2023-06-01 |
| PublicationDate_xml | – month: 06 year: 2023 text: June 2023 |
| PublicationDecade | 2020 |
| PublicationPlace | United States |
| PublicationPlace_xml | – name: United States – name: Washington |
| PublicationTitle | Biometrics |
| PublicationTitleAlternate | Biometrics |
| PublicationYear | 2023 |
| Publisher | Blackwell Publishing Ltd |
| Publisher_xml | – name: Blackwell Publishing Ltd |
| References | 2004; 88 2018; 122 1995; 90 2017; 81 2017; 27 1986; 34 2019; 34 1978; 73 1988; 103 2008; 9 1975 2008; 56 1951 2014; 29 2008; 147 2017; 157 2012; 107 2003; 31 1983; 11 1955 2014; 109 2011; 106 1961; 1 2007; 8 2019 2005; 4 2018 1956; 27 2020; 48 2016; 62 2017 2011; 21 1962; 24 2009; 37 2009; 104 1990; 5 2016; 44 2012; 40 Li (2024011411372650800_biom13686-bib-0024) 2017 Jiang (2024011411372650800_biom13686-bib-0014) 2009; 37 Langfelder (2024011411372650800_biom13686-bib-0020) 2008; 9 Mestre (2024011411372650800_biom13686-bib-0029) 2008; 56 Robbins (2024011411372650800_biom13686-bib-0030) 1951 Stein (2024011411372650800_biom13686-bib-0037) 1986; 34 Zhang (2024011411372650800_biom13686-bib-0041) 2003; 31 Schäfer (2024011411372650800_biom13686-bib-0035) 2005; 4 Laird (2024011411372650800_biom13686-bib-0018) 1978; 73 Donoho (2024011411372650800_biom13686-bib-0005) 1995; 90 Feng (2024011411372650800_biom13686-bib-0009) 2018; 122 Fan (2024011411372650800_biom13686-bib-0008) 2008; 147 Huang (2024011411372650800_biom13686-bib-0012) 2017; 157 Lindley (2024011411372650800_biom13686-bib-0025) 1962; 24 Liu (2024011411372650800_biom13686-bib-0027) 2017; 81 Dey (2024011411372650800_biom13686-bib-0004) 2018 Stein (2024011411372650800_biom13686-bib-0036) 1975 Saul (2024011411372650800_biom13686-bib-0034) 2017; 27 Lindsay (2024011411372650800_biom13686-bib-0026) 1983; 11 Efron (2024011411372650800_biom13686-bib-0006) 2014; 29 Rothman (2024011411372650800_biom13686-bib-0032) 2009; 104 Johnstone (2024011411372650800_biom13686-bib-0015) 2017 Varin (2024011411372650800_biom13686-bib-0039) 2011; 21 Cai (2024011411372650800_biom13686-bib-0003) 2011; 106 Robbins (2024011411372650800_biom13686-bib-0031) 1955 Efron (2024011411372650800_biom13686-bib-0007) 2019; 34 Stigler (2024011411372650800_biom13686-bib-0038) 1990; 5 Zhang (2024011411372650800_biom13686-bib-0042) 2005; 4 Bun (2024011411372650800_biom13686-bib-0002) 2016; 62 Lam (2024011411372650800_biom13686-bib-0019) 2016; 44 Markowetz (2024011411372650800_biom13686-bib-0028) 2007; 8 Saha (2024011411372650800_biom13686-bib-0033) 2020; 48 Fourdrinier (2024011411372650800_biom13686-bib-0010) 2018 James (2024011411372650800_biom13686-bib-0013) 1961 Brown (2024011411372650800_biom13686-bib-0001) 2009; 37 Ledoit (2024011411372650800_biom13686-bib-0021) 2004; 88 Xue (2024011411372650800_biom13686-bib-0040) 2012; 107 Koenker (2024011411372650800_biom13686-bib-0017) 2014; 109 Ledoit (2024011411372650800_biom13686-bib-0022) 2019 Higham (2024011411372650800_biom13686-bib-0011) 1988; 103 Kiefer (2024011411372650800_biom13686-bib-0016) 1956; 27 Ledoit (2024011411372650800_biom13686-bib-0023) 2012; 40 |
| References_xml | – volume: 62 start-page: 7475 year: 2016 end-page: 7490 article-title: Rotational invariant estimator for general noisy matrices publication-title: IEEE Transactions on Information Theory – volume: 122 start-page: 80 year: 2018 end-page: 91 article-title: Approximate nonparametric maximum likelihood for mixture models: a convex optimization approach to fitting arbitrary multivariate mixing distributions publication-title: Computational Statistics & Data Analysis – volume: 27 start-page: 887 year: 1956 end-page: 906 article-title: Consistency of the maximum likelihood estimator in the presence of infinitely many incidental parameters publication-title: The Annals of Mathematical Statistics – volume: 104 start-page: 177 year: 2009 end-page: 186 article-title: Generalized thresholding of large covariance matrices publication-title: Journal of the American Statistical Association – volume: 11 start-page: 86 year: 1983 end-page: 94 article-title: The geometry of mixture likelihoods: a general theory publication-title: The Annals of Statistics – volume: 34 start-page: 1373 year: 1986 end-page: 1403 article-title: Lectures on the theory of estimation of many parameters publication-title: Journal of Soviet Mathematics – volume: 40 start-page: 1024 year: 2012 end-page: 1060 article-title: Nonlinear shrinkage estimation of large‐dimensional covariance matrices publication-title: The Annals of Statistics – volume: 44 start-page: 928 year: 2016 end-page: 953 article-title: Nonparametric eigenvalue‐regularized precision or covariance matrix estimator publication-title: The Annals of Statistics – start-page: 157 year: 1955 end-page: 164 article-title: An empirical Bayes approach to statistics – volume: 106 start-page: 672 year: 2011 end-page: 684 article-title: Adaptive thresholding for sparse covariance matrix estimation publication-title: Journal of the American Statistical Association – volume: 103 start-page: 103 year: 1988 end-page: 118 article-title: Computing a nearest symmetric positive semidefinite matrix publication-title: Linear Algebra and its Applications – volume: 88 start-page: 365 year: 2004 end-page: 411 article-title: A well‐conditioned estimator for large‐dimensional covariance matrices publication-title: Journal of Multivariate Analysis – volume: 37 start-page: 1647 year: 2009 end-page: 1684 article-title: General maximum likelihood empirical Bayes estimation of normal means publication-title: The Annals of Statistics – volume: 109 start-page: 674 year: 2014 end-page: 685 article-title: Convex optimization, shape constraints, compound decisions, and empirical Bayes rules publication-title: Journal of the American Statistical Association – volume: 9 start-page: 1 year: 2008 end-page: 13 article-title: WGCNA: an R package for weighted correlation network analysis publication-title: BMC Bioinformatics – year: 2018 – volume: 21 start-page: 5 year: 2011 end-page: 42 article-title: An overview of composite likelihood methods publication-title: Statistica Sinica – volume: 4 year: 2005 article-title: A general framework for weighted gene co‐expression network analysis publication-title: Statistical Applications in Genetics and Molecular Biology – volume: 34 start-page: 177 year: 2019 end-page: 201 article-title: Bayes, Oracle Bayes and empirical Bayes publication-title: Statistical Science – volume: 48 start-page: 738 year: 2020 end-page: 762 article-title: On the nonparametric maximum likelihood estimator for Gaussian location mixture densities with application to Gaussian denoising publication-title: Annals of Statistics – volume: 157 start-page: 45 year: 2017 end-page: 52 article-title: A calibration method for non‐positive definite covariance matrix in multivariate data analysis publication-title: Journal of Multivariate Analysis – volume: 81 start-page: 50 year: 2017 end-page: 55 article-title: A covariance matrix shrinkage method with Toeplitz rectified target for DOA estimation under the uniform linear array publication-title: AEU‐International Journal of Electronics and Communications – volume: 73 start-page: 805 year: 1978 end-page: 811 article-title: Nonparametric maximum likelihood estimation of a mixing distribution publication-title: Journal of the American Statistical Association – volume: 90 start-page: 1200 year: 1995 end-page: 1224 article-title: Adapting to unknown smoothness via wavelet shrinkage publication-title: Journal of the American Statistical Association – volume: 147 start-page: 186 year: 2008 end-page: 197 article-title: High dimensional covariance matrix estimation using a factor model publication-title: Journal of Econometrics – volume: 56 start-page: 5353 year: 2008 end-page: 5368 article-title: On the asymptotic behavior of the sample estimates of eigenvalues and eigenvectors of covariance matrices publication-title: IEEE Transactions on Signal Processing – volume: 29 start-page: 285 year: 2014 end-page: 301 article-title: Two modeling strategies for empirical Bayes estimation publication-title: Statistical Science – volume: 5 start-page: 147 year: 1990 end-page: 155 article-title: The 1988 Neyman memorial lecture: a Galtonian perspective on shrinkage estimators publication-title: Statistical Science – volume: 31 start-page: 379 year: 2003 end-page: 390 article-title: Compound decision theory and empirical Bayes methods publication-title: The Annals of Statistics – start-page: 1 year: 2017 end-page: 8 article-title: Estimation of high dimensional covariance matrices by shrinkage algorithms – year: 1951 article-title: Asymptotically subminimax solutions of compound statistical decision problems – volume: 37 start-page: 1685 year: 2009 end-page: 1704 article-title: Nonparametric empirical Bayes and compound decision approaches to estimation of a high‐dimensional vector of normal means publication-title: The Annals of Statistics – volume: 4 year: 2005 article-title: A shrinkage approach to large‐scale covariance matrix estimation and implications for functional genomics publication-title: Statistical Applications in Genetics and Molecular Biology – volume: 24 start-page: 265 year: 1962 end-page: 296 article-title: Discussion on Professor Stein's paper publication-title: Journal of the Royal Statistical Society: Series B (Methodological) – year: 2017 – volume: 107 start-page: 1480 year: 2012 end-page: 1491 article-title: Positive‐definite ‐penalized estimation of large covariance matrices publication-title: Journal of the American Statistical Association – volume: 1 start-page: 367 year: 1961 end-page: 379 article-title: Estimation with quadratic loss – volume: 27 start-page: 959 year: 2017 end-page: 972 article-title: Transcriptional regulatory dynamics drive coordinated metabolic and neural response to social challenge in mice publication-title: Genome Research – volume: 8 start-page: S5 year: 2007 article-title: Inferring cellular networks – a review publication-title: BMC Bioinformatics – year: 1975 article-title: Estimation of a covariance matrix – year: 2019 – volume: 29 start-page: 285 year: 2014 ident: 2024011411372650800_biom13686-bib-0006 article-title: Two modeling strategies for empirical Bayes estimation publication-title: Statistical Science doi: 10.1214/13-STS455 – volume: 11 start-page: 86 year: 1983 ident: 2024011411372650800_biom13686-bib-0026 article-title: The geometry of mixture likelihoods: a general theory publication-title: The Annals of Statistics doi: 10.1214/aos/1176346059 – volume-title: Shrinkage estimation year: 2018 ident: 2024011411372650800_biom13686-bib-0010 doi: 10.1007/978-3-030-02185-6 – volume: 31 start-page: 379 year: 2003 ident: 2024011411372650800_biom13686-bib-0041 article-title: Compound decision theory and empirical Bayes methods publication-title: The Annals of Statistics doi: 10.1214/aos/1051027872 – volume: 37 start-page: 1685 year: 2009 ident: 2024011411372650800_biom13686-bib-0001 article-title: Nonparametric empirical Bayes and compound decision approaches to estimation of a high-dimensional vector of normal means publication-title: The Annals of Statistics doi: 10.1214/08-AOS630 – volume: 9 start-page: 1 year: 2008 ident: 2024011411372650800_biom13686-bib-0020 article-title: WGCNA: an R package for weighted correlation network analysis publication-title: BMC Bioinformatics doi: 10.1186/1471-2105-9-559 – volume: 4 year: 2005 ident: 2024011411372650800_biom13686-bib-0035 article-title: A shrinkage approach to large-scale covariance matrix estimation and implications for functional genomics publication-title: Statistical Applications in Genetics and Molecular Biology doi: 10.2202/1544-6115.1175 – volume: 27 start-page: 887 year: 1956 ident: 2024011411372650800_biom13686-bib-0016 article-title: Consistency of the maximum likelihood estimator in the presence of infinitely many incidental parameters publication-title: The Annals of Mathematical Statistics doi: 10.1214/aoms/1177728066 – volume: 104 start-page: 177 year: 2009 ident: 2024011411372650800_biom13686-bib-0032 article-title: Generalized thresholding of large covariance matrices publication-title: Journal of the American Statistical Association doi: 10.1198/jasa.2009.0101 – volume: 73 start-page: 805 year: 1978 ident: 2024011411372650800_biom13686-bib-0018 article-title: Nonparametric maximum likelihood estimation of a mixing distribution publication-title: Journal of the American Statistical Association doi: 10.1080/01621459.1978.10480103 – volume: 103 start-page: 103 year: 1988 ident: 2024011411372650800_biom13686-bib-0011 article-title: Computing a nearest symmetric positive semidefinite matrix publication-title: Linear Algebra and its Applications doi: 10.1016/0024-3795(88)90223-6 – volume: 37 start-page: 1647 year: 2009 ident: 2024011411372650800_biom13686-bib-0014 article-title: General maximum likelihood empirical Bayes estimation of normal means publication-title: The Annals of Statistics doi: 10.1214/08-AOS638 – start-page: 367 volume-title: Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability year: 1961 ident: 2024011411372650800_biom13686-bib-0013 article-title: Estimation with quadratic loss – volume-title: Quadratic shrinkage for large covariance matrices year: 2019 ident: 2024011411372650800_biom13686-bib-0022 doi: 10.2139/ssrn.3486378 – volume: 4 year: 2005 ident: 2024011411372650800_biom13686-bib-0042 article-title: A general framework for weighted gene co-expression network analysis publication-title: Statistical Applications in Genetics and Molecular Biology doi: 10.2202/1544-6115.1128 – volume: 48 start-page: 738 year: 2020 ident: 2024011411372650800_biom13686-bib-0033 article-title: On the nonparametric maximum likelihood estimator for Gaussian location mixture densities with application to Gaussian denoising publication-title: Annals of Statistics doi: 10.1214/19-AOS1817 – volume-title: Gaussian estimation: sequence and wavelet models year: 2017 ident: 2024011411372650800_biom13686-bib-0015 – volume: 157 start-page: 45 year: 2017 ident: 2024011411372650800_biom13686-bib-0012 article-title: A calibration method for non-positive definite covariance matrix in multivariate data analysis publication-title: Journal of Multivariate Analysis doi: 10.1016/j.jmva.2017.03.001 – volume-title: 39th Annual Meeting IMS, Atlanta, GA, 1975 year: 1975 ident: 2024011411372650800_biom13686-bib-0036 article-title: Estimation of a covariance matrix – volume: 122 start-page: 80 year: 2018 ident: 2024011411372650800_biom13686-bib-0009 article-title: Approximate nonparametric maximum likelihood for mixture models: a convex optimization approach to fitting arbitrary multivariate mixing distributions publication-title: Computational Statistics & Data Analysis doi: 10.1016/j.csda.2018.01.006 – volume: 81 start-page: 50 year: 2017 ident: 2024011411372650800_biom13686-bib-0027 article-title: A covariance matrix shrinkage method with Toeplitz rectified target for DOA estimation under the uniform linear array publication-title: AEU-International Journal of Electronics and Communications – volume: 147 start-page: 186 year: 2008 ident: 2024011411372650800_biom13686-bib-0008 article-title: High dimensional covariance matrix estimation using a factor model publication-title: Journal of Econometrics doi: 10.1016/j.jeconom.2008.09.017 – volume: 34 start-page: 177 year: 2019 ident: 2024011411372650800_biom13686-bib-0007 article-title: Bayes, Oracle Bayes and empirical Bayes publication-title: Statistical Science – start-page: 1 volume-title: 2017 20th International Conference on Information Fusion (Fusion) year: 2017 ident: 2024011411372650800_biom13686-bib-0024 article-title: Estimation of high dimensional covariance matrices by shrinkage algorithms – start-page: 157 volume-title: Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability year: 1955 ident: 2024011411372650800_biom13686-bib-0031 article-title: An empirical Bayes approach to statistics – volume: 44 start-page: 928 year: 2016 ident: 2024011411372650800_biom13686-bib-0019 article-title: Nonparametric eigenvalue-regularized precision or covariance matrix estimator publication-title: The Annals of Statistics doi: 10.1214/15-AOS1393 – volume: 24 start-page: 265 year: 1962 ident: 2024011411372650800_biom13686-bib-0025 article-title: Discussion on Professor Stein's paper publication-title: Journal of the Royal Statistical Society: Series B (Methodological) – volume: 56 start-page: 5353 year: 2008 ident: 2024011411372650800_biom13686-bib-0029 article-title: On the asymptotic behavior of the sample estimates of eigenvalues and eigenvectors of covariance matrices publication-title: IEEE Transactions on Signal Processing doi: 10.1109/TSP.2008.929662 – volume: 62 start-page: 7475 year: 2016 ident: 2024011411372650800_biom13686-bib-0002 article-title: Rotational invariant estimator for general noisy matrices publication-title: IEEE Transactions on Information Theory doi: 10.1109/TIT.2016.2616132 – volume-title: bioRxiv year: 2018 ident: 2024011411372650800_biom13686-bib-0004 article-title: Corshrink: empirical bayes shrinkage estimation of correlations, with applications doi: 10.1101/368316 – volume: 34 start-page: 1373 year: 1986 ident: 2024011411372650800_biom13686-bib-0037 article-title: Lectures on the theory of estimation of many parameters publication-title: Journal of Soviet Mathematics doi: 10.1007/BF01085007 – volume: 21 start-page: 5 year: 2011 ident: 2024011411372650800_biom13686-bib-0039 article-title: An overview of composite likelihood methods publication-title: Statistica Sinica – volume: 90 start-page: 1200 year: 1995 ident: 2024011411372650800_biom13686-bib-0005 article-title: Adapting to unknown smoothness via wavelet shrinkage publication-title: Journal of the American Statistical Association doi: 10.1080/01621459.1995.10476626 – volume-title: Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability year: 1951 ident: 2024011411372650800_biom13686-bib-0030 article-title: Asymptotically subminimax solutions of compound statistical decision problems doi: 10.1525/9780520411586-011 – volume: 109 start-page: 674 year: 2014 ident: 2024011411372650800_biom13686-bib-0017 article-title: Convex optimization, shape constraints, compound decisions, and empirical Bayes rules publication-title: Journal of the American Statistical Association doi: 10.1080/01621459.2013.869224 – volume: 88 start-page: 365 year: 2004 ident: 2024011411372650800_biom13686-bib-0021 article-title: A well-conditioned estimator for large-dimensional covariance matrices publication-title: Journal of Multivariate Analysis doi: 10.1016/S0047-259X(03)00096-4 – volume: 106 start-page: 672 year: 2011 ident: 2024011411372650800_biom13686-bib-0003 article-title: Adaptive thresholding for sparse covariance matrix estimation publication-title: Journal of the American Statistical Association doi: 10.1198/jasa.2011.tm10560 – volume: 5 start-page: 147 year: 1990 ident: 2024011411372650800_biom13686-bib-0038 article-title: The 1988 Neyman memorial lecture: a Galtonian perspective on shrinkage estimators publication-title: Statistical Science doi: 10.1214/ss/1177012274 – volume: 27 start-page: 959 year: 2017 ident: 2024011411372650800_biom13686-bib-0034 article-title: Transcriptional regulatory dynamics drive coordinated metabolic and neural response to social challenge in mice publication-title: Genome Research doi: 10.1101/gr.214221.116 – volume: 107 start-page: 1480 year: 2012 ident: 2024011411372650800_biom13686-bib-0040 article-title: Positive-definite l1-penalized estimation of large covariance matrices publication-title: Journal of the American Statistical Association doi: 10.1080/01621459.2012.725386 – volume: 8 start-page: S5 year: 2007 ident: 2024011411372650800_biom13686-bib-0028 article-title: Inferring cellular networks – a review publication-title: BMC Bioinformatics doi: 10.1186/1471-2105-8-S6-S5 – volume: 40 start-page: 1024 year: 2012 ident: 2024011411372650800_biom13686-bib-0023 article-title: Nonlinear shrinkage estimation of large-dimensional covariance matrices publication-title: The Annals of Statistics doi: 10.1214/12-AOS989 |
| SSID | ssj0009502 |
| Score | 2.4030504 |
| Snippet | Covariance matrix estimation is a fundamental statistical task in many applications, but the sample covariance matrix is suboptimal when the sample size is... |
| SourceID | proquest pubmed crossref wiley |
| SourceType | Aggregation Database Index Database Enrichment Source Publisher |
| StartPage | 1201 |
| SubjectTerms | Analysis of covariance Animals Bayes Theorem Biostatistics compound decision theory Computer Simulation Covariance matrix Data analysis Eigenvalues Estimation Gene Regulatory Networks genes Genomics g‐modeling Mice nonparametric maximum likelihood Nonparametric statistics Research methodology Sample Size separable decision rule sequence analysis shrinkage variance covariance matrix |
| Title | A compound decision approach to covariance matrix estimation |
| URI | https://onlinelibrary.wiley.com/doi/abs/10.1111%2Fbiom.13686 https://www.ncbi.nlm.nih.gov/pubmed/35499364 https://www.proquest.com/docview/2827420273 https://www.proquest.com/docview/2658645204 https://www.proquest.com/docview/2849881162 |
| Volume | 79 |
| WOSCitedRecordID | wos000799422000001&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: 1541-0420 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0009502 issn: 0006-341X databaseCode: DRFUL dateStart: 19990101 isFulltext: true titleUrlDefault: https://onlinelibrary.wiley.com providerName: Wiley-Blackwell |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1ZS8QwEB48QR881ms9loq-KBR6ZNMUfFmPRUFXEZV9K02TPOmuuLui_96Zpq0uiiC-lEImkCYzyTedyTcA-02dejIS2jWeCl3mB8qVmcTN0BivmYVxGuTZFg-XUacjut34ZgKOyrswlh-i-uFGlpHv12TgqRx8MXK6nk5JWoJPwrTvhxHpdMBuvlDuepYrnLK7mN8tyEkpj-ez7_hx9A1jjkPW_MxpL_5vtEuwUGBNp2WVYxkmdK8Gs7b65HsN5q8qytZBDeYIdlrW5hU4ajmUa04llxxVVOFxSvpxZ9jH1ld0skljnCci-X9ziK3DXoNchfv22d3JuVvUWXAzOp9dJSKlAymY5ExHHsXHOcfFNYgtuNKx9CUzsfGkHxg_Rn8lQByTGZ1poRkLw3ANpnr9nt4Ah2ujRaSbFN1hXqZEjHBLNVODXTmPVB0OyulOsoKEnGphPCalM0ITleQTVYe9SvbZUm_8KLVdrlpSmN8gwSGiy09UPXXYrZrRcCgakvZ0f4QyiL0oquuxX2QEi4XAjwnqsG41ohpKSJ51yLH3Yb7wv4wxOb64vsrfNv8ivAVzVNzeJqZtw9TwZaR3YCZ7RW14aeTKjs-oKxowfXrbvr_8ACI7AwU |
| linkProvider | Wiley-Blackwell |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1ZSwMxEB60KuqDR73quaIvCgt7ZLNZ8KUepWJbRVT6tnQ3yZO2Yg_03zuz2a6KIohvC5lANplJvslMvgE4DFTHSUKhbO1I32auJ-0kTXAz1NoJUj_qeFm2xUMjbLVEux3d5Lk59BbG8EMUF25kGdl-TQZOF9KfrJzep1OWluCTMMVQj4ISTJ3f1u4bn1h3HUMXTglezG3n_KSUyvPR--uJ9A1mfkWt2bFTW_zngJdgIcebVtUoyDJMqG4ZZkwFyrcyzDcL2tZ-GeYIehrm5hU4qVqUb05llyyZV-KxxhTk1qCHrSN0tElrrCci-n-1iLHDPIVchfvaxd1Z3c5rLdgpndG2FKFUXiJYwpkKHYqRc44LrBFfcKmixE2YjrSTuJ52I_RZPMQyqVapEoox3_fXoNTtddUGWFxpJUIVUISHOakUEUIuGXQ0duU8lBU4Gs93nOZE5FQP4zEeOyQ0UXE2URU4KGSfDf3Gj1Lb42WLcxPsxzhEdPuJrqcC-0UzGg9FRDpd1RuiDOIviuw67BcZwSIh8Ge8CqwblSiG4pN37XPsfZyt_C9jjE8vr5vZ1-ZfhPdgtn7XbMSNy9bVFsxRsXuTqLYNpcHLUO3AdDpCzXjZzXX_HQeyBfo |
| linkToPdf | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LT8MwDLZgPDQOPMarPIvgAlKlPtI0lbjwmkCwsQOg3aq1SU6wobEh-PfYTVeGQEiIW6U6kpvYyefa-QxwEKqOm0ZCOdqVgcM8XzppluJmqLUbZkHc8fNqi4ebqNkU7XbcKmpz6C6M4Ycof7iRZ-T7NTm4epZ6zMvpfjpVaQk-CVMsxE2WiJ1Za4xz1zVk4VTexbx2wU5KhTyfY7-eR99A5lfMmh869YV_qrsI8wXatE-MeSzBhOrWYMb0n3yvwVyjJG19qUGVgKfhbV6G4xObqs2p6ZItiz489oiA3B708O0rhtlkM_YT0fy_2cTXYS5CrsB9_eLu7NIpOi04GZ3QjhSRVH4qWMqZilzKkHOOy6sRXXCp4tRLmY61m3q-9mKMWHxEMplWmRKKsSAIVqHS7XXVOthcaSUiFVJ-h7mZFDECLhl2NA7lPJIWHI7mO8kKGnLqhvGYjMIRmqgknygL9kvZZ0O-8aPU1mjZksIBXxJUEYN-IuuxYK98ja5D-ZBOV_WGKIPoi_K6LvtFRrBYCPwY34I1YxKlKgHF1gHH0Uf5yv-iY3J6ddvInzb-IrwLs63zenJz1bzehCp1ujdValtQGfSHahums1c0jP5Obvgf4QID4w |
| 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=A+compound+decision+approach+to+covariance+matrix+estimation&rft.jtitle=Biometrics&rft.au=Xin%2C+Huiqin&rft.au=Zhao%2C+Sihai+Dave&rft.date=2023-06-01&rft.issn=0006-341X&rft.eissn=1541-0420&rft.volume=79&rft.issue=2&rft.spage=1201&rft.epage=1212&rft_id=info:doi/10.1111%2Fbiom.13686&rft.externalDBID=10.1111%252Fbiom.13686&rft.externalDocID=BIOM13686 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0006-341X&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0006-341X&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0006-341X&client=summon |