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arXiv · 2206.10856

Ensemble minimaxity of James-Stein estimators

Yuzo Maruyama·Lawrence D. Brown·Edward I. George
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Abstract

This article discusses estimation of a multivariate normal mean based on heteroscedastic observations. Under heteroscedasticity, estimators shrinking more on the coordinates with larger variances, seem desirable. Although they are not necessarily minimax in the ordinary sense, 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.

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Yuzo Maruyama, Lawrence D. Brown, Edward I. George. 2022-06-22. Ensemble minimaxity of James-Stein estimators. https://arxiv.org/abs/2206.10856

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