Robust Hypothesis Testing with $\alpha$-Divergence

TL;DR

This paper introduces a robust minimax hypothesis test based on $ ext{alpha}$-divergence, deriving decision rules and least favorable distributions, with simplified design under symmetry and validated through simulations.

Contribution

It proposes a novel robust hypothesis testing framework using $ ext{alpha}$-divergence and characterizes the saddle point conditions with explicit derivations.

Findings

Derived robust decision rules and least favorable distributions.

Simplified design procedure under symmetry conditions.

Validated theoretical results with simulation experiments.

Abstract

A robust minimax test for two composite hypotheses, which are determined by the neighborhoods of two nominal distributions with respect to a set of distances - called $\alpha-$divergence distances, is proposed. Sion's minimax theorem is adopted to characterize the saddle value condition. Least favorable distributions, the robust decision rule and the robust likelihood ratio test are derived. If the nominal probability distributions satisfy a symmetry condition, the design procedure is shown to be simplified considerably. The parameters controlling the degree of robustness are bounded from above and the bounds are shown to be resulting from a solution of a set of equations. The simulations performed evaluate and exemplify the theoretical derivations.