Explicit maximum likelihood estimators for certain patterned covariance matrices
Titel:
Explicit maximum likelihood estimators for certain patterned covariance matrices
Auteur:
Rogers, G. S. Young, D. L.
Verschenen in:
Communications in statistics
Paginering:
Jaargang 6 (1977) nr. 2 pagina's 121-133
Jaar:
1977
Inhoud:
Given a random sample of size N from a p-variate normal distribution with mean vector μ and covariance matrix Σ, max-imum likelihood estimation of Σ is considered when both Σ and Σ-1 have linear structure, that is, when [image omitted] and [image omitted] where G1,…,Gm and H1,…,Hn are sets of known p×p symmetric linearly independent matrices. Theorems are given relating m and n and the sets G1,…,Gm and H1,…,Hn in the general case and when Σ is totally reducible. Explicit maximum likelihood estimators of σ1,…,σ m are found when m = n, and several examples, are given.
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