Testing hypothesis on transition distributions of a Markov sequence

Abstract We propose a method for testing hypothesis on parametric family of transition probabilities of a Markov sequence, when the asymptotic distribution of the empirical processes involved is, largely, independent from the specific form of the parametric family. We first consider function-parametric empirical process for the Markov sequence and describe its weak limit as a certain projection. Then we establish equivalence between testing different families of transition probabilities and show how the empirical process for one testing problem can be transformed into empirical process in another testing problem. This creates wide equivalence classes and allows distribution free testing.