Estimation of a non-centrality parameter under Stein-type-like losses

Abstract

Abstract The estimation of the non-centrality parameter of a chi-squared distribution, although simple to state, leads to difficulties, both for frequentist and Bayesian inferences. We propose in this paper a family of admissible improper Bayes estimators and study the minimax behavior of these estimators under Stein loss and its symmetric version. Although no formal minimaxity result can be stated, we show through comparison with a family of natural estimators that the (restricted) minimax estimator deduced from this study is quite acceptable.