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Ensemble minimaxity of James-Stein estimators Maruyama, Yuzo


We consider estimation of a heteroscedastic multivariate normal mean. Under heteroscedasticity, estimators shrinking more on the coordinates with larger variances, seem desirable. However, they are not necessarily ordinary minimax. We show that such James-Stein type estimators can be ensemble minimax, minimax with respect to the ensemble risk, related to empirical Bayes perspective of Efron and Morris. This is a joint work with Larry Brown and Ed George.

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