Estimation in multivariate elliptically contoured linear models .2.

For a multivariate elliptically contoured random matrix Y with mean mu is an element of S-1 square S-2 and covariance proportional to Sigma(j=1)(k) V-j X Sigma(j), explicit formulae for the best linear unbiased estimator of mu, the best quadratic unbiased estimators of the Sigma(j)'s, are obtained, where X is the Kronecker product, S-1 and S-2 are known linear subspaces of R-n and R-p, respectively, and S-1 square S-2 is the linear space spanned by xy' with x is an element of S-1 and y is an element of S-2. The distributions of the estimators are also studied. The multivariate components of variance models and certain growth curve models are special cases of this linear model. For illustration, our results are applied to the balanced multivariate mixed models.