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The James-Stein estimator for the mean of an independent multivariate normal with equal variances is obtained by adaptive shrinkage of the sample mean estimator. This estimator dominates the mean estimator for dimensions greater or equal than three. In this work, we present variations of this estimator for the independent normal case with unequal variances and for the general case where the estimator is obtained using the Mahalanobis' metric. Geometric justications and a study of the behavior of these estimators by computational simulation for dimension three are presented using the mean square error as a measure of quality.
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