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Article: EM-type algorithms for computing restricted MLEs in multivariate normal distributions and multivariate t-distributions

TitleEM-type algorithms for computing restricted MLEs in multivariate normal distributions and multivariate t-distributions
Authors
Issue Date2008
PublisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/csda
Citation
Computational Statistics and Data Analysis, 2008, v. 52 n. 10, p. 4768-4778 How to Cite?
AbstractConstrained parameter problems arise in a variety of statistical applications but they have been most resistant to solution. This paper proposes methodology for estimating restricted parameters in multivariate normal distributions with known or unknown covariance matrix. The proposed method thus provides a solution to an open problem to find penalized estimation for linear inverse problem with positivity restrictions [Vardi, Y., Lee, D. 1993. From image deblurring to optimal investments: Maximum likelihood solutions for positive linear inverse problems (with discussion). Journal of the Royal Statistical Society, Series B 55, 569-612]. By first considering the simplest bound constraints and then generalizing them to linear inequality constraints, we propose a unified EM-type algorithm for estimating constrained parameters via data augmentation. The key idea is to introduce a sequence of latent variables such that the complete-data model belongs to the exponential family, hence, resulting in a simple E-step and an explicit M-step. Furthermore, we extend restricted multivariate normal distribution to multivariate t-distribution with constrained parameters to obtain robust estimation. With the proposed algorithms, standard errors can be calculated by bootstrapping. The proposed method is appealing for its simplicity and ease of implementation and its applicability to a wide class of parameter restrictions. Three real data sets are analyzed to illustrate different aspects of the proposed methods. Finally, the proposed algorithm is applied to linear inverse problems with possible negativity restrictions and is evaluated numerically. © 2008 Elsevier B.V. All rights reserved.
Persistent Identifierhttp://hdl.handle.net/10722/59853
ISSN
2015 Impact Factor: 1.179
2015 SCImago Journal Rankings: 1.283
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorTian, GLen_HK
dc.contributor.authorNg, KWen_HK
dc.contributor.authorTan, Men_HK
dc.date.accessioned2010-05-31T03:58:49Z-
dc.date.available2010-05-31T03:58:49Z-
dc.date.issued2008en_HK
dc.identifier.citationComputational Statistics and Data Analysis, 2008, v. 52 n. 10, p. 4768-4778en_HK
dc.identifier.issn0167-9473en_HK
dc.identifier.urihttp://hdl.handle.net/10722/59853-
dc.description.abstractConstrained parameter problems arise in a variety of statistical applications but they have been most resistant to solution. This paper proposes methodology for estimating restricted parameters in multivariate normal distributions with known or unknown covariance matrix. The proposed method thus provides a solution to an open problem to find penalized estimation for linear inverse problem with positivity restrictions [Vardi, Y., Lee, D. 1993. From image deblurring to optimal investments: Maximum likelihood solutions for positive linear inverse problems (with discussion). Journal of the Royal Statistical Society, Series B 55, 569-612]. By first considering the simplest bound constraints and then generalizing them to linear inequality constraints, we propose a unified EM-type algorithm for estimating constrained parameters via data augmentation. The key idea is to introduce a sequence of latent variables such that the complete-data model belongs to the exponential family, hence, resulting in a simple E-step and an explicit M-step. Furthermore, we extend restricted multivariate normal distribution to multivariate t-distribution with constrained parameters to obtain robust estimation. With the proposed algorithms, standard errors can be calculated by bootstrapping. The proposed method is appealing for its simplicity and ease of implementation and its applicability to a wide class of parameter restrictions. Three real data sets are analyzed to illustrate different aspects of the proposed methods. Finally, the proposed algorithm is applied to linear inverse problems with possible negativity restrictions and is evaluated numerically. © 2008 Elsevier B.V. All rights reserved.en_HK
dc.languageengen_HK
dc.publisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/csdaen_HK
dc.relation.ispartofComputational Statistics and Data Analysisen_HK
dc.rightsComputational Statistics and Data Analysis. Copyright © Elsevier BV.-
dc.titleEM-type algorithms for computing restricted MLEs in multivariate normal distributions and multivariate t-distributionsen_HK
dc.typeArticleen_HK
dc.identifier.emailTian, GL: gltian@hku.hken_HK
dc.identifier.emailNg, KW: kaing@hkucc.hku.hken_HK
dc.identifier.authorityTian, GL=rp00789en_HK
dc.identifier.authorityNg, KW=rp00765en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1016/j.csda.2008.03.022en_HK
dc.identifier.scopuseid_2-s2.0-44349158963en_HK
dc.identifier.hkuros148988en_HK
dc.identifier.hkuros163558-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-44349158963&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume52en_HK
dc.identifier.issue10en_HK
dc.identifier.spage4768en_HK
dc.identifier.epage4778en_HK
dc.identifier.isiWOS:000257377100020-
dc.publisher.placeNetherlandsen_HK
dc.identifier.scopusauthoridTian, GL=25621549400en_HK
dc.identifier.scopusauthoridNg, KW=7403178774en_HK
dc.identifier.scopusauthoridTan, M=7401464906en_HK

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