Robust Hypothesis Testing with a Relative Entropy Tolerance

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.

14 pages, 5 figures, submitted to the IEEE Transactions on Information Theory, July 2007, revised April 2008

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