English

Ensemble minimaxity of James-Stein estimators

Statistics Theory 2022-06-23 v1 Methodology Statistics Theory

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.

Keywords

Cite

@article{arxiv.2206.10856,
  title  = {Ensemble minimaxity of James-Stein estimators},
  author = {Yuzo Maruyama and Lawrence D. Brown and Edward I. George},
  journal= {arXiv preprint arXiv:2206.10856},
  year   = {2022}
}