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Nonparametric estimation of component distributions in a multivariate mixture

Zhou, Xiao-Hua; Hall, Peter

Description

Suppose k-variate data are drawn from a mixture of two distributions, each having independent components. It is desired to estimate the univariate marginal distributions in each of the products, as well as the mixing proportion. This is the setting of two-class, fully parametrized latent models that has been proposed for estimating the distributions of medical test results when disease status is unavailable. The problem is one of inference in a mixture of distributions without training data,...[Show more]

dc.contributor.authorZhou, Xiao-Hua
dc.contributor.authorHall, Peter
dc.date.accessioned2016-02-05T04:59:12Z
dc.date.available2016-02-05T04:59:12Z
dc.identifier.issn0090-5364
dc.identifier.urihttp://hdl.handle.net/1885/97931
dc.description.abstractSuppose k-variate data are drawn from a mixture of two distributions, each having independent components. It is desired to estimate the univariate marginal distributions in each of the products, as well as the mixing proportion. This is the setting of two-class, fully parametrized latent models that has been proposed for estimating the distributions of medical test results when disease status is unavailable. The problem is one of inference in a mixture of distributions without training data, and until now it has been tackled only in a fully parametric setting. We investigate the possibility of using nonparametric methods. Of course, when k=1 the problem is not identifiable from a nonparametric viewpoint. We show that the problem is "almost" identifiable when k=2; there, the set of all possible representations can be expressed, in terms of any one of those representations, as a two-parameter family. Furthermore, it is proved that when k≥3 the problem is nonparametrically identifiable under particularly mild regularity conditions. In this case we introduce root-n consistent nonparametric estimators of the 2k univariate marginal distributions and the mixing proportion. Finite-sample and asymptotic properties of the estimators are described.
dc.publisherInstitute of Mathematical Statistics
dc.rights© Institute of Mathematical Statistics, 2003. http://www.sherpa.ac.uk/romeo/issn/0090-5364..."author can archive publisher's version/PDF. On author's personal website or open access repository" from SHERPA/RoMEO site (as at 5/02/16).
dc.sourceThe Annals of Statistics
dc.subjectKeywords: Biased bootstrap; Distribution estimation; Empirical likelihood; Identification; Latent model; Multivariate analysis; Nonparametric maximum likelihood; Root-n consistency
dc.titleNonparametric estimation of component distributions in a multivariate mixture
dc.typeJournal article
local.description.notesImported from ARIES
local.description.refereedYes
local.identifier.citationvolume31
dc.date.issued2003
local.identifier.absfor010405
local.identifier.ariespublicationMigratedxPub5244
local.publisher.urlhttp://imstat.org/en/index.html
local.type.statusPublished Version
local.contributor.affiliationHall, Peter, College of Physical and Mathematical Sciences, CPMS Mathematical Sciences Institute, Centre for Mathematics and Its Applications, The Australian National University
local.contributor.affiliationZhou, Xiangting, College of Physical and Mathematical Sciences, CPMS Research School of Chemistry, RSC General, The Australian National University
local.bibliographicCitation.issue1
local.bibliographicCitation.startpage201
local.bibliographicCitation.lastpage224
local.identifier.doi10.1214/aos/1046294462
dc.date.updated2016-02-24T09:48:39Z
local.identifier.scopusID2-s2.0-21144453941
CollectionsANU Research Publications

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