Constructing Bayes Minimax Estimators through Integral Transformations

TL;DR

This paper introduces a novel method for constructing Bayes minimax estimators for multivariate normal means using integral transformations like the I-transform and Laplace transform, offering a unified approach with practical examples.

Contribution

It presents a new technique leveraging integral transforms to derive Bayes minimax estimators, expanding the toolkit for statistical estimation under quadratic loss.

Findings

Effective construction of Bayes minimax estimators demonstrated

Integral transform methods simplify derivation process

Examples show improved estimator properties

Abstract

The problem of Bayes minimax estimation for the mean of a multivariate normal distribution under quadratic loss has attracted significant attention recently. These estimators have the advantageous property of being admissible, similar to Bayes procedures, while also providing the conservative risk guarantees typical of frequentist methods. This paper demonstrates that Bayes minimax estimators can be derived using integral transformation techniques, specifically through the \( I \)-transform and the Laplace transform, as long as appropriate spherical priors are selected. Several illustrative examples are included to highlight the effectiveness of the proposed approach.