Abstract
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 and 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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