A Generalized Poor-Verdu Error Bound for Multihypothesis Testing

Abstract

A lower bound on the minimum error probability for multihypothesis testing is established. The bound, which is expressed in terms of the cumulative distribution function of the tilted posterior hypothesis distribution given the observation with tilting parameter theta >= 1, generalizes an earlier bound due the Poor and Verdu (1995). A sufficient condition is established under which the new bound (minus a multiplicative factor) provides the exact error probability asymptotically in theta. Examples illustrating the new bound are also provided.