Statistical inference for finite Markov chains based on divergences

Abstract

We consider statistical data forming sequences of states of stationary finite irreducible Markov chains, and draw statistical inference about the transition matrix. The inference consists in estimation of parameters of transition probabilities and testing simple and composite hypotheses about them. The inference is based on statistics which are suitable weighted sums of normed phi-divergences of theoretical row distributions, evaluated at suitable points, and observed empirical row distributions. The asymptotic distribution of minimum phi-divergence estimators is obtained, as well as critical values of asymptotically alpha-level tests.