Hypothesis testing for arbitrarily varying source with exponential-type constraint

The problem of hypothesis testing, which is to decide between two alternative explanations for the observed data, is one of the standard problems in statistics. A discrete memoryless source (DMS) is a sequence of i.i.d random variables. The distribution of the DMS is either P₁ or P₂. When a sample is emitted from the source, the observer attempts to decide which hypothesis of H₁:P₁ or H₂:P₂ is correct. The main concern of this problem is to determine the best asymptotic exponent of the second kind of the error probability when the first kind of the error probability is (1) fixed (2) less than 2^-nr. These are specified by (1) the well-known lemma of Stein (Blahut 1974) the theorem of Hoeffding (1965), Blahut (1974), Csiszar and Longo (1971) for the hypothesis testing problem with exponential-type constraint. DMS is an ideal model. A more robust model is an arbitrarily varying source (AVS), where the source distribution may vary within a certain set of distribution from one time instant to the next. The varying behavior of the distribution of AVS is not known exactly, and there are only two alternatives. We consider the problem of hypothesis testing for AVS in the same way for DMS, and determine the best asymptotic exponent of the second kind of the error probability when the first kind of the error probability is (1) fixed (2) less than 2^-nr