File Download
  Links for fulltext
     (May Require Subscription)
Supplementary

Article: On estimation of the noise variance in high dimensional probabilistic principal component analysis

TitleOn estimation of the noise variance in high dimensional probabilistic principal component analysis
Authors
KeywordsGoodness of fit
High dimensional data
Noise variance estimator
Number of principal components
Probabilistic principal component analysis
Random-matrix theory
Issue Date2017
PublisherWiley-Blackwell Publishing Ltd. The Journal's web site is located at http://www.blackwellpublishing.com/journals/RSSB
Citation
Journal of the Royal Statistical Society. Series B: Statistical Methodology, 2017, v. 79 n. 1, p. 51-67 How to Cite?
AbstractWe develop new statistical theory for probabilistic principal component analysis models in high dimensions. The focus is the estimation of the noise variance, which is an important and unresolved issue when the number of variables is large in comparison with the sample size. We first unveil the reasons for an observed downward bias of the maximum likelihood estimator of the noise variance when the data dimension is high. We then propose a bias-corrected estimator by using random-matrix theory and establish its asymptotic normality. The superiority of the new and bias-corrected estimator over existing alternatives is checked by Monte Carlo experiments with various combinations of (p,n) (the dimension and sample size). Next, we construct a new criterion based on the bias-corrected estimator to determine the number of the principal components, and a consistent estimator is obtained. Its good performance is confirmed by a simulation study and real data analysis. The bias-corrected estimator is also used to derive new asymptotics for the related goodness-of-fit statistic under the high dimensional scheme.
Persistent Identifierhttp://hdl.handle.net/10722/231313
ISSN
2023 Impact Factor: 3.1
2023 SCImago Journal Rankings: 4.330
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorPassemier, D-
dc.contributor.authorLi, Z-
dc.contributor.authorYao, JJ-
dc.date.accessioned2016-09-20T05:22:15Z-
dc.date.available2016-09-20T05:22:15Z-
dc.date.issued2017-
dc.identifier.citationJournal of the Royal Statistical Society. Series B: Statistical Methodology, 2017, v. 79 n. 1, p. 51-67-
dc.identifier.issn1369-7412-
dc.identifier.urihttp://hdl.handle.net/10722/231313-
dc.description.abstractWe develop new statistical theory for probabilistic principal component analysis models in high dimensions. The focus is the estimation of the noise variance, which is an important and unresolved issue when the number of variables is large in comparison with the sample size. We first unveil the reasons for an observed downward bias of the maximum likelihood estimator of the noise variance when the data dimension is high. We then propose a bias-corrected estimator by using random-matrix theory and establish its asymptotic normality. The superiority of the new and bias-corrected estimator over existing alternatives is checked by Monte Carlo experiments with various combinations of (p,n) (the dimension and sample size). Next, we construct a new criterion based on the bias-corrected estimator to determine the number of the principal components, and a consistent estimator is obtained. Its good performance is confirmed by a simulation study and real data analysis. The bias-corrected estimator is also used to derive new asymptotics for the related goodness-of-fit statistic under the high dimensional scheme.-
dc.languageeng-
dc.publisherWiley-Blackwell Publishing Ltd. The Journal's web site is located at http://www.blackwellpublishing.com/journals/RSSB-
dc.relation.ispartofJournal of the Royal Statistical Society. Series B: Statistical Methodology-
dc.rightsThis is the accepted version of the following article: Journal of the Royal Statistical Society. Series B: Statistical Methodology, 2017, v. 79 n. 1, p. 51-67, which has been published in final form at http://onlinelibrary.wiley.com/wol1/doi/10.1111/rssb.12153/abstract-
dc.subjectGoodness of fit-
dc.subjectHigh dimensional data-
dc.subjectNoise variance estimator-
dc.subjectNumber of principal components-
dc.subjectProbabilistic principal component analysis-
dc.subjectRandom-matrix theory-
dc.titleOn estimation of the noise variance in high dimensional probabilistic principal component analysis-
dc.typeArticle-
dc.identifier.emailYao, JJ: jeffyao@hku.hk-
dc.identifier.authorityYao, JJ=rp01473-
dc.description.naturepostprint-
dc.identifier.doi10.1111/rssb.12153-
dc.identifier.scopuseid_2-s2.0-84953449796-
dc.identifier.hkuros263174-
dc.identifier.volume79-
dc.identifier.issue1-
dc.identifier.spage51-
dc.identifier.epage67-
dc.identifier.isiWOS:000392486000004-
dc.publisher.placeUnited Kingdom-
dc.identifier.issnl1369-7412-

Export via OAI-PMH Interface in XML Formats


OR


Export to Other Non-XML Formats