Title: A curious likelihood identity for the multivariate t-distribution
Abstract: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 maximu...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.Read More
Publication Year: 1994
Publication Date: 1994-01-01
Language: en
Type: article
Indexed In: ['crossref']
Access and Citation
Cited By Count: 100
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