Convex Optimization, Shape Constraints, Compound Decisions, and Empirical Bayes Rules
Estimation of mixture densities for the classical Gaussian compound decision problem and their associated (empirical) Bayes rules is considered from two new perspectives. The first, motivated by Brown and Greenshtein, introduces a nonparametric maximum likelihood estimator of the mixture density sub...
Uloženo v:
| Vydáno v: | Journal of the American Statistical Association Ročník 109; číslo 506; s. 674 - 685 |
|---|---|
| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Alexandria
Taylor & Francis
01.06.2014
Taylor & Francis Group, LLC Taylor & Francis Ltd |
| Témata: | |
| ISSN: | 1537-274X, 0162-1459, 1537-274X |
| On-line přístup: | Získat plný text |
| Tagy: |
Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
|
| Abstract | Estimation of mixture densities for the classical Gaussian compound decision problem and their associated (empirical) Bayes rules is considered from two new perspectives. The first, motivated by Brown and Greenshtein, introduces a nonparametric maximum likelihood estimator of the mixture density subject to a monotonicity constraint on the resulting Bayes rule. The second, motivated by Jiang and Zhang, proposes a new approach to computing the Kiefer–Wolfowitz nonparametric maximum likelihood estimator for mixtures. In contrast to prior methods for these problems, our new approaches are cast as convex optimization problems that can be efficiently solved by modern interior point methods. In particular, we show that the reformulation of the Kiefer–Wolfowitz estimator as a convex optimization problem reduces the computational effort by several orders of magnitude for typical problems , by comparison to prior EM-algorithm based methods, and thus greatly expands the practical applicability of the resulting methods. Our new procedures are compared with several existing empirical Bayes methods in simulations employing the well-established design of Johnstone and Silverman. Some further comparisons are made based on prediction of baseball batting averages. A Bernoulli mixture application is briefly considered in the penultimate section. |
|---|---|
| AbstractList | Estimation of mixture densities for the classical Gaussian compound decision problem and their associated (empirical) Bayes rules is considered from two new perspectives. The first, motivated by Brown and Greenshtein, introduces a nonparametric maximum likelihood estimator of the mixture density subject to a monotonicity constraint on the resulting Bayes rule. The second, motivated by Jiang and Zhang, proposes a new approach to computing the Kiefer-Wolfowitz nonparametric maximum likelihood estimator for mixtures. In contrast to prior methods for these problems, our new approaches are cast as convex optimization problems that can be efficiently solved by modern interior point methods. In particular, we show that the reformulation of the Kiefer-Wolfowitz estimator as a convex optimization problem reduces the computational effort by several orders of magnitude for typical problems, by comparison to prior EM-algorithm based methods, and thus greatly expands the practical applicability of the resulting methods. Our new procedures are compared with several existing empirical Bayes methods in simulations employing the well-established design of Johnstone and Silverman. Some further comparisons are made based on prediction of baseball batting averages. A Bernoulli mixture application is briefly considered in the penultimate section. |
| Author | Koenker, Roger Mizera, Ivan |
| Author_xml | – sequence: 1 givenname: Roger surname: Koenker fullname: Koenker, Roger – sequence: 2 givenname: Ivan surname: Mizera fullname: Mizera, Ivan |
| BookMark | eNqFkk1v1DAQhiPUSvSDfwAiEhcO3cUfseNwQbAttFKlSpSVuFmzzhi8SuxgJ8D21-MlgFAv9cUznvedsR77uDjwwWNRPKVkSYkirwiVjFaiWTJC-VLJhrHqUXFEBa8XrK4-H_wXPy6OU9qSvGqljor1Kvjv-LO8GUbXuzsYXfBn5e1XGLDMpTRGcH5MZznphzD5tjxH41JW5TPI6UU_uOgMdOU72GEqP04dptPi0EKX8Mmf_aRYv7_4tLpcXN98uFq9vV4YQfm4YHxjDTWAFTbYAjQWJfK6pi2KxnCKNke4UYACuDQt3QAQK5AqSRQXLT8pXs59hxi-TZhG3btksOvAY5iSpopwohjnMktf3JNuwxR9vp2mUhFG6gwwq6pZZWJIKaLVQ3Q9xJ2mRO9Z67-s9Z61nlln2-t7NuPG3yz3_LqHzM9m8zaNIf4byCpW1bQRuf5mrjtvQ-zhR4hdq0fYdSHaCD4_h-YPTHg-d7AQNHyJ2bC-zQKZf4ESkhH-C_F0rJo |
| CODEN | JSTNAL |
| CitedBy_id | crossref_primary_10_1080_01621459_2022_2093729 crossref_primary_10_1017_S0266466617000299 crossref_primary_10_1080_01621459_2020_1802284 crossref_primary_10_1214_19_STS707 crossref_primary_10_1214_24_BA1496 crossref_primary_10_1214_19_STS706 crossref_primary_10_1214_24_BA1498 crossref_primary_10_1093_biomet_asv067 crossref_primary_10_1016_j_csda_2018_01_006 crossref_primary_10_1111_insr_12098 crossref_primary_10_1080_01621459_2021_2008403 crossref_primary_10_1080_01621459_2024_2421994 crossref_primary_10_1111_obes_12400 crossref_primary_10_1002_sta4_38 crossref_primary_10_1257_aer_20230700 crossref_primary_10_1002_sim_70195 crossref_primary_10_1186_s13059_021_02418_8 crossref_primary_10_1080_07350015_2015_1052457 crossref_primary_10_1214_20_AOS1950 crossref_primary_10_1016_j_optlastec_2023_110139 crossref_primary_10_1111_sjos_12778 crossref_primary_10_1214_19_STS754 crossref_primary_10_1214_22_AOS2207 crossref_primary_10_1111_biom_12619 crossref_primary_10_1093_jrsssb_qkae040 crossref_primary_10_1002_sam_11689 crossref_primary_10_1002_jae_2530 crossref_primary_10_1111_rssb_12490 crossref_primary_10_1214_19_STS709 crossref_primary_10_1214_19_STS708 crossref_primary_10_1109_LSP_2024_3376205 crossref_primary_10_1007_s11222_025_10686_8 crossref_primary_10_3982_ECTA18597 crossref_primary_10_1002_sim_10150 crossref_primary_10_1214_19_AOS1873 crossref_primary_10_1093_biomet_asw053 crossref_primary_10_1080_10618600_2019_1689985 crossref_primary_10_1111_ectj_12092 crossref_primary_10_1080_07350015_2021_1984928 crossref_primary_10_3390_math13162639 crossref_primary_10_1214_15_AOS1377 crossref_primary_10_1214_19_STS674REJ crossref_primary_10_1016_j_spl_2018_05_012 crossref_primary_10_1080_03610926_2020_1766501 crossref_primary_10_1214_24_AOS2416 crossref_primary_10_1214_24_STS940 crossref_primary_10_1002_sam_11472 crossref_primary_10_1002_sta4_154 crossref_primary_10_1002_sam_11554 crossref_primary_10_1016_j_csda_2020_107130 crossref_primary_10_1093_biomet_asac019 crossref_primary_10_1080_01621459_2021_1967164 crossref_primary_10_1080_01621459_2022_2120401 crossref_primary_10_3150_18_BEJ1096 crossref_primary_10_1016_j_jeconom_2023_01_028 crossref_primary_10_1093_biomet_asaf007 crossref_primary_10_1093_biostatistics_kxw041 crossref_primary_10_1214_18_STS673 crossref_primary_10_1080_00949655_2022_2109634 crossref_primary_10_1214_18_STS674 crossref_primary_10_1162_rest_a_00812 crossref_primary_10_1214_21_BA1263 crossref_primary_10_1080_01621459_2021_1962328 crossref_primary_10_1002_soej_12395 crossref_primary_10_1111_biom_13686 crossref_primary_10_1214_19_AOS1817 crossref_primary_10_1016_j_csda_2017_08_003 crossref_primary_10_1016_j_jeconom_2016_05_018 crossref_primary_10_1080_03610918_2019_1622720 crossref_primary_10_3982_ECTA19304 crossref_primary_10_3390_pharmaceutics13010042 |
| Cites_doi | 10.1111/j.1467-9574.1983.tb00796.x 10.1006/aima.1994.1002 10.2140/pjm.1971.39.439 10.1214/aoms/1177728066 10.1214/10-IMSCOLL618 10.1016/0304-4076(84)90075-7 10.1214/09-AOS790 10.1198/jasa.2011.tm11181 10.1111/j.1467-9469.2007.00585.x 10.1214/08-AOS630 10.1515/9781400873173 10.1111/j.1467-9469.2007.00588.x 10.1214/10-AOS814 10.1214/10-AOS840 10.1214/009053604000000030 10.1017/CBO9780511761362 10.1214/aos/1015345958 10.1016/j.csda.2006.12.013 10.1214/08-AOS638 10.1111/j.1467-9868.2010.00753.x 10.1080/01621459.1978.10480103 10.1214/07-AOAS138 10.3150/08-BEJ141 10.1214/aos/1176346059 10.1214/aos/1032526949 |
| ContentType | Journal Article |
| Copyright | 2014 American Statistical Association 2014 Copyright © 2014 American Statistical Association Copyright Taylor & Francis Ltd. Jun 2014 |
| Copyright_xml | – notice: 2014 American Statistical Association 2014 – notice: Copyright © 2014 American Statistical Association – notice: Copyright Taylor & Francis Ltd. Jun 2014 |
| DBID | FBQ AAYXX CITATION 8BJ FQK JBE K9. 7S9 L.6 |
| DOI | 10.1080/01621459.2013.869224 |
| DatabaseName | AGRIS CrossRef International Bibliography of the Social Sciences (IBSS) International Bibliography of the Social Sciences International Bibliography of the Social Sciences ProQuest Health & Medical Complete (Alumni) AGRICOLA AGRICOLA - Academic |
| DatabaseTitle | CrossRef International Bibliography of the Social Sciences (IBSS) ProQuest Health & Medical Complete (Alumni) AGRICOLA AGRICOLA - Academic |
| DatabaseTitleList | AGRICOLA International Bibliography of the Social Sciences (IBSS) |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Statistics |
| EISSN | 1537-274X |
| EndPage | 685 |
| ExternalDocumentID | 3681333451 10_1080_01621459_2013_869224 24247195 869224 US201600085620 |
| Genre | Article Feature |
| GroupedDBID | -DZ -~X .-4 ..I .7F .GJ .QJ 07G 0BK 0R~ 1OL 29L 2AX 30N 3R3 3V. 4.4 5GY 5RE 692 7WY 7X7 85S 88E 88I 8AF 8C1 8FE 8FG 8FI 8FJ 8FL 8G5 8R4 8R5 AAAVI AAAVZ AABCJ AAENE AAFWJ AAIKQ AAJMT AAKBW AALDU AAMIU AAPUL AAQRR ABBHK ABCCY ABEFU ABEHJ ABFAN ABFIM ABJCF ABJNI ABJVF ABLIJ ABLJU ABPEM ABPFR ABPPZ ABQHQ ABRLO ABTAI ABUWG ABXUL ABXYU ABYAD ABYWD ACAGQ ACGFO ACGFS ACGOD ACIWK ACMTB ACNCT ACTIO ACTMH ACTWD ACUBG ADBBV ADCVX ADGTB ADLSF ADODI ADULT AEGYZ AEISY AELPN AENEX AEOZL AEPSL AEUMN AEUPB AEYOC AFFNX AFKRA AFOLD AFSUE AFVYC AFWLO AFXHP AFXKK AGCQS AGDLA AGLEN AGMYJ AGROQ AHDLD AHMOU AI. AIHXQ AIJEM AIRXU AKBVH AKOOK ALCKM ALMA_UNASSIGNED_HOLDINGS ALQZU AMATQ AMXXU AQRUH AQUVI AVBZW AZQEC BCCOT BENPR BEZIV BGLVJ BKNYI BKOMP BLEHA BPHCQ BPLKW BVXVI C06 CCCUG CCPQU CJ0 CRFIH CS3 D0L DGEBU DKSSO DMQIW DQDLB DSRWC DU5 DWIFK DWQXO E.L EBS ECEWR EFSUC EJD E~A E~B F20 F5P FBQ FEDTE FJW FRNLG FUNRP FVMVE FVPDL FYUFA GNUQQ GROUPED_ABI_INFORM_COMPLETE GROUPED_ABI_INFORM_RESEARCH GTTXZ GUQSH HCIFZ HF~ HGD HMCUK HQ6 HVGLF HZ~ H~9 H~P IAO IEA IGG IOF IPNFZ IPO IVXBP J.P JAAYA JAS JBMMH JBZCM JENOY JHFFW JKQEH JLEZI JLXEF JMS JPL JSODD JST K60 K6~ K9- KQ8 KYCEM L6V LJTGL LU7 M0C M0R M0T M1P M2O M2P M4Z M7S MS~ MVM MW2 N95 NA5 NHB NUSFT NY~ O9- OFU OK1 P-O P2P PADUT PQBIZ PQQKQ PRG PROAC PSQYO PTHSS Q2X QCRFL RIG RNANH RNS ROSJB RTWRZ RWL RXW S-T S0X SA0 SJN SNACF TAE TAQ TEJ TFL TFMCV TFT TFW TN5 TOXWX TTHFI U5U UB9 UKHRP UPT UQL UT5 UU3 V1K VH1 VOH WH7 WHG WZA XFK YQT YXB YYM YYP ZCG ZGI ZGOLN ZUP ZXP ~S~ AAGDL AAHBH AAHIA AAWIL ABAWQ ABPAQ ABPQH ABUFD ABXSQ ACHJO ADMHG ADXHL AFRVT AGLNM AHDZW AIHAF AIYEW ALRMG AMVHM AQTUD AWYRJ H13 IPSME TASJS TBQAZ TDBHL TUROJ ADYSH ALIPV AMPGV AAYXX CITATION 8BJ FQK JBE K9. 7S9 L.6 |
| ID | FETCH-LOGICAL-c513t-23bfc1cae4e9edaa9fe6e3771de59c31ef1deeb8ae5a36cd1baa0f5e1860835d3 |
| IEDL.DBID | TFW |
| ISICitedReferencesCount | 105 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000338236000019&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 1537-274X 0162-1459 |
| IngestDate | Thu Oct 02 23:59:16 EDT 2025 Sat Nov 29 17:10:33 EST 2025 Tue Nov 18 22:07:54 EST 2025 Sat Nov 29 03:56:39 EST 2025 Fri May 30 11:48:46 EDT 2025 Mon Oct 20 23:43:55 EDT 2025 Wed Dec 27 19:14:39 EST 2023 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 506 |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c513t-23bfc1cae4e9edaa9fe6e3771de59c31ef1deeb8ae5a36cd1baa0f5e1860835d3 |
| Notes | http://dx.doi.org/10.1080/01621459.2013.869224 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-1 ObjectType-Feature-2 content type line 23 |
| PQID | 1680207459 |
| PQPubID | 41715 |
| PageCount | 12 |
| ParticipantIDs | proquest_journals_1680207459 crossref_primary_10_1080_01621459_2013_869224 informaworld_taylorfrancis_310_1080_01621459_2013_869224 jstor_primary_24247195 fao_agris_US201600085620 proquest_miscellaneous_1803082336 crossref_citationtrail_10_1080_01621459_2013_869224 |
| PublicationCentury | 2000 |
| PublicationDate | 2014-06-01 |
| PublicationDateYYYYMMDD | 2014-06-01 |
| PublicationDate_xml | – month: 06 year: 2014 text: 2014-06-01 day: 01 |
| PublicationDecade | 2010 |
| PublicationPlace | Alexandria |
| PublicationPlace_xml | – name: Alexandria |
| PublicationTitle | Journal of the American Statistical Association |
| PublicationYear | 2014 |
| Publisher | Taylor & Francis Taylor & Francis Group, LLC Taylor & Francis Ltd |
| Publisher_xml | – name: Taylor & Francis – name: Taylor & Francis Group, LLC – name: Taylor & Francis Ltd |
| References | cit0011 cit0012 cit0031 cit0010 Rockafellar R.T. (cit0025) 1970 Johnstone I. (cit0016) 2004 Koenker R. (cit0018) 2013 Jiang W. (cit0015) 2010 Robbins H. (cit0024) 1956 cit0019 cit0017 cit0013 cit0014 cit0022 cit0023 cit0021 cit0008 cit0009 cit0006 cit0028 cit0007 cit0029 cit0004 cit0026 cit0005 cit0002 cit0003 |
| References_xml | – ident: cit0029 doi: 10.1111/j.1467-9574.1983.tb00796.x – ident: cit0002 doi: 10.1006/aima.1994.1002 – ident: cit0026 doi: 10.2140/pjm.1971.39.439 – ident: cit0017 doi: 10.1214/aoms/1177728066 – start-page: 263 volume-title: Borrowing Strength: Theory Powering Applications: A Festschrift for Lawrence D. Brown (Vol. 6) year: 2010 ident: cit0015 doi: 10.1214/10-IMSCOLL618 – ident: cit0013 doi: 10.1016/0304-4076(84)90075-7 – volume-title: Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability (Vol. I) year: 1956 ident: cit0024 – ident: cit0006 doi: 10.1214/09-AOS790 – ident: cit0010 doi: 10.1198/jasa.2011.tm11181 – ident: cit0031 doi: 10.1111/j.1467-9469.2007.00585.x – ident: cit0005 doi: 10.1214/08-AOS630 – volume-title: Convex Analysis year: 1970 ident: cit0025 doi: 10.1515/9781400873173 – ident: cit0012 doi: 10.1111/j.1467-9469.2007.00588.x – ident: cit0019 doi: 10.1214/10-AOS814 – ident: cit0028 doi: 10.1214/10-AOS840 – start-page: 1594 year: 2004 ident: cit0016 publication-title: The Annals of Statistics doi: 10.1214/009053604000000030 – ident: cit0009 doi: 10.1017/CBO9780511761362 – ident: cit0011 doi: 10.1214/aos/1015345958 – ident: cit0003 doi: 10.1016/j.csda.2006.12.013 – ident: cit0014 doi: 10.1214/08-AOS638 – ident: cit0007 doi: 10.1111/j.1467-9868.2010.00753.x – year: 2013 ident: cit0018 publication-title: R package version 0.31, – ident: cit0021 doi: 10.1080/01621459.1978.10480103 – ident: cit0004 doi: 10.1214/07-AOAS138 – ident: cit0008 doi: 10.3150/08-BEJ141 – ident: cit0022 doi: 10.1214/aos/1176346059 – ident: cit0023 doi: 10.1214/aos/1032526949 |
| SSID | ssj0000788 |
| Score | 2.5282445 |
| Snippet | Estimation of mixture densities for the classical Gaussian compound decision problem and their associated (empirical) Bayes rules is considered from two new... |
| SourceID | proquest crossref jstor informaworld fao |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 674 |
| SubjectTerms | Algorithms Baseball Bayes estimators Bayes rule Bayesian analysis Bernoulli Hypothesis Constraints Convex analysis Density estimation Empirical Bayes Estimating techniques Estimation methods Estimators Interior points Iterative solutions Kiefer-Wolfowitz maximum likelihood estimator Maximum likelihood estimation Mixture models Mixtures Normal distribution Objective functions Optimization prediction Rules Scientific method Statistics system optimization Theory and Methods |
| Title | Convex Optimization, Shape Constraints, Compound Decisions, and Empirical Bayes Rules |
| URI | https://www.tandfonline.com/doi/abs/10.1080/01621459.2013.869224 https://www.jstor.org/stable/24247195 https://www.proquest.com/docview/1680207459 https://www.proquest.com/docview/1803082336 |
| Volume | 109 |
| WOSCitedRecordID | wos000338236000019&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: PRVAWR databaseName: Taylor & Francis Online Journals customDbUrl: eissn: 1537-274X dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0000788 issn: 1537-274X databaseCode: TFW dateStart: 19220301 isFulltext: true titleUrlDefault: https://www.tandfonline.com providerName: Taylor & Francis |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1Lb9QwELag4tAL76qBgozEsYb1euPERyhdcUAF0S70Zo2dMSC1u6tmF8G_Z8ZJlgICJLjlYVv2eDweJzPfJ8Tj4BpSE5dUZWNUEwtOAZ0zVMCmrEZgRjFTsrx7VR0d1aen7s2lLH4Oq-QzdOqAIrKt5sUNoR0i4p6Sl8L42pxmos2T2jrahsgI087PK_Nk-v67Ka4y8SRXUFxjyJ37TSM_7E1XEyx-wi8dYhZ_sdt5M5re-P9h3BTXe0dUPus055a4gvPbYpt9zw66-Y6YHXBE-hf5mqzKeZ-uuS-PP8ISJfN8ZnaJVbsv2aYwO5N80RP20DPqlTw8X37KCCTyOXzFVr5dn2F7V8ymhycHL1XPwqBiqc1KjU1IUUfACTpsAFxCi6aqdIOli0ZjoisMNWAJxsZGB4BRKlHXlt27xuyIrflijrtCBg5lZW4kdHQw0RUEcm-cwQBjgCbVhTCD_H3sIcp5LGdeD0imvcw8y8x3MiuE2tRadhAdfym_S1Pr4QNZUT87HjPGHnuedjwqRH15vv0qfzVJHcWJN39udSfrxqYLnHdTaVcWYm9QFt_bh9ZrW5OfXlEbhXi0eU0rm3_XwBwXaypTd1hCxt77927dF9t0N-mC2_bE1upijQ_EtfiZlOniYV4t3wCn4gzw |
| linkProvider | Taylor & Francis |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV3db9MwED-xgcRexue0wAAj8bhAXTdO_Ahj1RClINbC3qyLcwGkra2WdoL_nrt8lC8BEuItSmzLH-e7s3P3-wE8yl3BYuLKOLUhxAOLLkY-Z8Q5FUnaQ9MLNSXLu1E6HmcnJ-5NG01YtWGVcoYuG6CIWlfL5pbL6C4k7gm7KQKwLXkm2jzOrGM7tAGXEza1Ap8_Gb7_pozTmnpSasRSpcue-00rP1injRLnPyGYdlGLv2ju2hwNr_2HgVyH7dYXVU8b4bkBl2h2E7bE_WzQm2_B9ECC0j-r16xYztqMzX11_BEXpITqsyaYWFb7StSKEDSp5y1nD7_jbqnDs8WnGoREPcMvVKm3q1OqbsN0eDg5OIpbIoY4JNos477Jy6AD0oAcFYiuJEsmTXVBiQtGU8lPlGdICRobCp0j9sqEdGbFwyvMDmzO5jPaBZVLNKvQI5Hjs4lOMWcPxxnKsY9YlFkEplsAH1qUchnLqdcdmGk7Z17mzDdzFkG8rrVoUDr-Un6X19bjB1akfnrcF5g9cT5tvxdB9v2C-2V9cVI2LCfe_LnVnVo41l2Q1JtUuySCvU5afKsiKq9txq56ym1E8HD9mTe3_LHBGc1XXCZr4ISMvfPv3XoAV48mr0Z-9GL88i5s8ZdBE-u2B5vL8xXdgyvhggXr_H69db4CtTIRGg |
| linkToPdf | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3db9MwED-xgdBe-J4WGGAkHheo68aJH2FbBWIqE1thb9bFOQ-kra3WFsF_z10-ygABErxF8Yfs8_l8Tu5-P4CnpatYTVxMcxtCOrDoUuR7RlpSleU9NL1QU7K8P8hHo-LkxB1eyuKXsEq5Q8cGKKK21bK5Z1XsIuKes5ci-NqSZqLNs8I6PobW4Cp7zlZ0_Hj44bstzmvmSWmRSpMuee43vfxwOK1FnP4EYNoFLf5iuOvTaHjz_-dxC260nqh60ajObbhCkzuwIc5ng918F8a7EpL-Rb1ls3Le5mvuqKOPOCMlRJ81vcRivqPEqAg9k9prGXv4HY9K7Z_PPtUQJOolfqW5erc8o_k9GA_3j3dfpS0NQxoybRZp35Qx6IA0IEcVootkyeS5rihzwWiK_ERlgZShsaHSJWIvZqQLK_5dZTZhfTKd0BaoUmJZhRyJHN9MdI4l-zfOUIl9xCoWCZhO_j60GOUylzOvOyjTVmZeZOYbmSWQrlrNGoyOv9Tf4qX1eMpm1I-P-gKyJ66n7fcSKC6vt1_Un01iw3HizZ973ax1YzUESbzJtcsS2O6UxbcGYu61LdhRz7mPBJ6sinlry_8anNB0yXWKBkzI2Pv_PqzHcP1wb-gPXo_ePIANLhg0gW7bsL64WNJDuBY-s15dPKo3zjdjbQ_M |
| 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=Convex+Optimization%2C+Shape+Constraints%2C+Compound+Decisions%2C+and+Empirical+Bayes+Rules&rft.jtitle=Journal+of+the+American+Statistical+Association&rft.au=Koenker%2C+Roger&rft.au=Mizera%2C+Ivan&rft.date=2014-06-01&rft.pub=Taylor+%26+Francis&rft.issn=1537-274X&rft.eissn=1537-274X&rft.volume=109&rft.issue=506&rft.spage=674&rft.epage=685&rft_id=info:doi/10.1080%2F01621459.2013.869224&rft.externalDocID=US201600085620 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1537-274X&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1537-274X&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1537-274X&client=summon |