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Constructing Bayes Minimax Estimators through Integral Transformations

Year: 2025

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2505.07649

Authors: Fourdrinier, Dominique, Strawderman, William E., Wells, Martin T.

Institutions: Laboratoire d'Informatique, du Traitement de l'Information et des Systèmes, Université de Rouen Normandie, Rutgers, The State University of New Jersey, Cornell University

Language: English

Topic: Statistical Distribution Estimation and Applications

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4417517331

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