Robust Hypothesis Testing with a Relative Entropy Tolerance

TL;DR

This paper develops a robust minimax hypothesis test that accounts for uncertainties in probability densities using relative entropy bounds, with applications demonstrated in noisy binary data transmission.

Contribution

It introduces a saddle point characterization for the minimax test and a nonlinear transformation to enhance robustness against density uncertainties.

Findings

The robust test effectively handles density uncertainties.

The method flattens the likelihood ratio near one for improved robustness.

Application to noisy binary data transmission demonstrates practical utility.

Abstract

This paper considers the design of a minimax test for two hypotheses where the actual probability densities of the observations are located in neighborhoods obtained by placing a bound on the relative entropy between actual and nominal densities. The minimax problem admits a saddle point which is characterized. The robust test applies a nonlinear transformation which flattens the nominal likelihood ratio in the vicinity of one. Results are illustrated by considering the transmission of binary data in the presence of additive noise.