Robustifying Empirical Bayes

TL;DR

This paper investigates methods to make empirical Bayes denoising more robust by reducing prior sensitivity and relaxing Gaussian noise assumptions, using classical statistical strategies.

Contribution

It introduces two robustification strategies for empirical Bayes denoising, adapting classical approaches to improve performance under model misspecification.

Findings

Reduced sensitivity to prior specification.

Effective handling of non-Gaussian noise.

Enhanced robustness of denoising procedures.

Abstract

Two strategies are explored for robustifying classical denoising procedures for the Gaussian sequence model. First, the Hodges and Lehmann (1952) restricted Bayes approach is used to reduce sensitivity to the specification of the initial prior distribution. Second, alternatives to the Gaussian noise assumption are explored. In both cases proposals of Huber (1964) and Mallows (1978) play a crucial role.