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...

We propose two families of maximally selected phi-divergence tests to detect a change in the probability vectors of a sequence of multinomial random variables with possibly different sizes. In addition, the proposed statistics can be used to estimate the location of the change-point. We derive...