Improved nonnegative estimation of multivariate components of variance

In this paper, we consider a multivariate one-way random effect model with equal replications. We propose non-negative definite estimators for 'between' and 'within' components of variance. Under the Stein loss function/Kullback-Leibler distance function, these estimators are shown to be better than the corresponding unbiased estimators. In particular, it is shown that the proposed restricted maximum likelihood estimator performs better than the unbiased as well as the truncated estimators proposed in this paper. Minimax and order-preserving minimax estimators are also proposed.

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