A curious likelihood identity for the multivariate t-distribution
作者:
John T. Kent,
David E. Tyler,
Yahuda. Vard,
期刊:
Communications in Statistics - Simulation and Computation
(Taylor Available online 1994)
卷期:
Volume 23,
issue 2
页码: 441-453
ISSN:0361-0918
年代: 1994
DOI:10.1080/03610919408813180
出版商: Marcel Dekker, Inc.
关键词: multivariate t-distribution;EM algorithm;robustness;uniqueness of maximum likelihood estimates
数据来源: Taylor
摘要:
It is shown that maximum likelihood estimates of the location vector and scatter matrix for a multivariate t-distribution in p dimensions with v≥1 degrees of freedom. can be identified with the maximum likelihood estimates for a scatter-only estimation problem from a (p+1)-dimensional multivariate the t-distribution with v−1>0 degrees of freedom. The t-distribution is only distribution for which this dual formulation is possible. Since the existence and uniqueness properties of maximum likelihood estimates are straightforward to prove for general scatter-only problems. we are able to immediately deduce existence and uniqueness results for the trickier location-scatter problem in the special case of the t-distribution. Each of these two formulations gives rise to an EM algorithm to maximize the likelihood. though the two algorithms are slightly different. The limiting Cauchy case v=1 requires some special treatment.
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