On Error Rate in Hypothesis Testing based on Universal Compression Algorithms

Identity test is a hypothesis test defined over the class of stationary and ergodic sources, to decide whether a sequence of random variables has originated from a known source τ or from an unknown source π. For an identity test proposed by Ryabko and Astola in 2005, that makes use of an arbitrary pointwise universal compression algorithm and π, the null distribution to define the critical region, we have studied the rate at which type-2 error goes to zero as sample size goes to infinity. A formal link is established between this rate and the redundancy rate of the compression algorithm in use for the class of Markov processes by an application of the method of types.