ADAPTATION IN MULTIVARIATE LOG-CONCAVE DENSITY ESTIMATION
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Feng, Oliver Y. | - |
dc.contributor.author | Guntuboyina, Adityanand | - |
dc.contributor.author | Kim, Arlene K. H. | - |
dc.contributor.author | Samworth, Richard J. | - |
dc.date.accessioned | 2021-08-30T03:27:32Z | - |
dc.date.available | 2021-08-30T03:27:32Z | - |
dc.date.created | 2021-06-19 | - |
dc.date.issued | 2021-02 | - |
dc.identifier.issn | 0090-5364 | - |
dc.identifier.uri | https://scholar.korea.ac.kr/handle/2021.sw.korea/49649 | - |
dc.description.abstract | We study the adaptation properties of the multivariate log-concave maximum likelihood estimator over three subclasses of log-concave densities. The first consists of densities with polyhedral support whose logarithms are piece-wise affine. The complexity of such densities f can be measured in terms of the sum Gamma(f) of the numbers of facets of the subdomains in the polyhedral subdivision of the support induced by f. Given n independent observations from a d-dimensional log-concave density with d is an element of {2, 3}, we prove a sharp oracle inequality, which in particular implies that the Kullback-Leibler risk of the log-concave maximum likelihood estimator for such densities is bounded above by Gamma(f)/n., up to a polylogarithmic factor. Thus, the rate can be essentially parametric, even in this multivariate setting. For the second type of adaptation, we consider densities that are bounded away from zero on a polytopal support; we show that up to polylogarithmic factors, the log-concave maximum likelihood estimator attains the rate n(-4/7) when d = 3, which is faster than the worst-case rate of n(-1/2). Finally, our third type of subclass consists of densities whose contours are well separated; these new classes are constructed to be affine invariant and turn out to contain a wide variety of densities, including those that satisfy Holder regularity conditions. Here, we prove another sharp oracle inequality, which reveals in particular that the log-concave maximum likelihood estimator attains a risk bound of order n(-min()(beta+3/)(beta+7, 4/7)) when d = 3 over the class of beta-Holder log-concave densities with beta > 1, again up to a polylogarithmic factor. | - |
dc.language | English | - |
dc.language.iso | en | - |
dc.publisher | INST MATHEMATICAL STATISTICS-IMS | - |
dc.subject | MAXIMUM-LIKELIHOOD-ESTIMATION | - |
dc.subject | LEAST-SQUARES | - |
dc.subject | GLOBAL RATES | - |
dc.subject | RISK BOUNDS | - |
dc.subject | CONVERGENCE | - |
dc.subject | POLYTOPES | - |
dc.subject | MODELS | - |
dc.title | ADAPTATION IN MULTIVARIATE LOG-CONCAVE DENSITY ESTIMATION | - |
dc.type | Article | - |
dc.contributor.affiliatedAuthor | Kim, Arlene K. H. | - |
dc.identifier.doi | 10.1214/20-AOS1950 | - |
dc.identifier.scopusid | 2-s2.0-85101287192 | - |
dc.identifier.wosid | 000614187400006 | - |
dc.identifier.bibliographicCitation | ANNALS OF STATISTICS, v.49, no.1, pp.129 - 153 | - |
dc.relation.isPartOf | ANNALS OF STATISTICS | - |
dc.citation.title | ANNALS OF STATISTICS | - |
dc.citation.volume | 49 | - |
dc.citation.number | 1 | - |
dc.citation.startPage | 129 | - |
dc.citation.endPage | 153 | - |
dc.type.rims | ART | - |
dc.type.docType | Article | - |
dc.description.journalClass | 1 | - |
dc.description.journalRegisteredClass | scie | - |
dc.description.journalRegisteredClass | scopus | - |
dc.relation.journalResearchArea | Mathematics | - |
dc.relation.journalWebOfScienceCategory | Statistics & Probability | - |
dc.subject.keywordPlus | MAXIMUM-LIKELIHOOD-ESTIMATION | - |
dc.subject.keywordPlus | LEAST-SQUARES | - |
dc.subject.keywordPlus | GLOBAL RATES | - |
dc.subject.keywordPlus | RISK BOUNDS | - |
dc.subject.keywordPlus | CONVERGENCE | - |
dc.subject.keywordPlus | POLYTOPES | - |
dc.subject.keywordPlus | MODELS | - |
dc.subject.keywordAuthor | Multivariate adaptation | - |
dc.subject.keywordAuthor | bracketing entropy | - |
dc.subject.keywordAuthor | log-concavity | - |
dc.subject.keywordAuthor | contour separation | - |
dc.subject.keywordAuthor | maximum likelihood estimation | - |
Items in ScholarWorks are protected by copyright, with all rights reserved, unless otherwise indicated.
(02841) 서울특별시 성북구 안암로 14502-3290-1114
COPYRIGHT © 2021 Korea University. All Rights Reserved.
Certain data included herein are derived from the © Web of Science of Clarivate Analytics. All rights reserved.
You may not copy or re-distribute this material in whole or in part without the prior written consent of Clarivate Analytics.