"Estimation of Variance and Covariance Components in Elliptically Contoured Distributions"

In this paper, we consider the problems of estimating the univariate and multivariate components of variance in elliptically contoured distribution (ECD) model in a decision-theoretic setup. Empirical Bayes or generalized Bayes estimators and several other positive or nonnegative (definite) estimators improving upon usual ANOVA (unbiased) estimators of the variance components are obtained. The robustness of these dominance results is also investigated, and it is shown that all dominance results under normal models remain true within a specific class of distributions.