A Review of Brown 1971 (in)admissibility results under scale mixtures of Gaussian priors

2021/10/05 by Yuzo Maruyama, Maruyama, Yuzo, William William +3
Computer Science · Mathematics · #62C15 #Bayesian Methods and Mixture Models #FOS: Mathematics #Statistical Distribution Estimation and Applications #Statistical Methods and Bayesian Inference #Statistics Theory (math.ST) #math.ST #msc:62C15 #stat.TH

paper · pdf · doi:10.48550/arxiv.2110.01945

18 pages

arxiv created 2021/10/05 · openalex publication_date 2021/10/05 · arxiv updated 2021/10/06 · openalex created_date 2022/11/29 · openalex updated_date 2026/07/28

Abstract

Brown's 1971 paper "Admissible estimators, recurrent diffusions and insoluble boundary value problems" is a landmark in the admissibility literature. It nearly completely settles the issue of admissibility/inadmissibility for estimating the mean of a multivariate normal distribution with identity covariance under sum of squared error loss. We revisit this wonderful tour de force on its 50th anniversary and present an alternative and more direct proof of the result for generalized Bayes estimators corresponding to priors which are a subclass of scale mixtures of spherical normals.

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