Asymptotically Optimal Hypothesis Testing with Memory Constraints

Abstract

The binary hypothesis testing problem of deciding between two Markov chains is formulated under memory constraints. The optimality criterion used in the exponential rate with which the probability of error approaches zero as the sample size tends to infinity. The optimal memory constrained test is shown to be the solution of a set of equations derived from suitable large deviation twistings of the transition matrices under the two hypotheses. A computational algorithm and some examples are given.