Inadmissibility of the maximum likelihood estimator of normal covariance matrices with the lattice conditional independence

Authors
Citation
Y. Konno, Inadmissibility of the maximum likelihood estimator of normal covariance matrices with the lattice conditional independence, J MULT ANAL, 79(1), 2001, pp. 33-51
Citations number
25
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF MULTIVARIATE ANALYSIS
ISSN journal
0047-259X → ACNP
Volume
79
Issue
1
Year of publication
2001
Pages
33 - 51
Database
ISI
SICI code
0047-259X(200110)79:1<33:IOTMLE>2.0.ZU;2-J
Abstract
Lattice conditional independence (LCI) models introduced by S. A. Andersson and M. D. Perlman (1993, Ann Statist, 21, 1318-1358) have the pleasant fea ture or admitting explicit maximum likelihood estimators and likelihood rat io test statistics. This is because the likelihood function and parameter s pace for a LCI model can be factored into products of conditional likelihoo d functions and parameter spaces, where the standard multivariate technique s can be applied. In this paper We consider the problem of estimating the c ovariance matrices under LCT restriction in a decision theoretic setup. The Stein loss function is used in this study and, using tile factorization me ntioned above, minimax estimators are obtained. Since the maximum likelihoo d estimator has constant risk and is different from the minimax estimator, this shows that the maximum likelihood estimator under LCI restriction inad missible. These results extend those obtained by W, James and C. Stein ( 19 60, in "Proceedings of the Fourth Berkeley Symposium on Mathematics, Statis tics, and Probability," Vol. 1, pp. 360 380, Univ. of California Press, Ber keley, CA) and D. K. Dey and C. Srinivasan ( 1985, Ann. Statist 13, 1581-15 91) for estimating normal covariance matrices to the LCI models. (C) 2001 A cademic Press.