Minimax Robust Hypothesis Testing

TL;DR

This paper develops a new minimax robust hypothesis testing framework that combines relative entropy-based robustness with Huber's method, applicable to fixed sample and sequential tests, and extends to robust estimation.

Contribution

It introduces a novel composite uncertainty model that unifies relative entropy and Huber's robustness, with proven saddle point existence and extensions to estimation.

Findings

The proposed scheme enhances robustness against modeling errors and outliers.

It guarantees saddle point existence under the composite uncertainty class.

Simulation results validate the effectiveness of the new robust testing approach.

Abstract

The minimax robust hypothesis testing problem for the case where the nominal probability distributions are subject to both modeling errors and outliers is studied in twofold. First, a robust hypothesis testing scheme based on a relative entropy distance is designed. This approach provides robustness with respect to modeling errors and is a generalization of a previous work proposed by Levy. Then, it is shown that this scheme can be combined with Huber's robust test through a composite uncertainty class, for which the existence of a saddle value condition is also proven. The composite version of the robust hypothesis testing scheme as well as the individual robust tests are extended to fixed sample size and sequential probability ratio tests. The composite model is shown to extend to robust estimation problems as well. Simulation results are provided to validate the proposed assertions.