Kybernetika

For data generated by stationary Markov chains there are considered estimates of chain parameters minimizing $\phi$--divergences between theoretical and empirical distributions of states. Consistency and asymptotic normality are established and the asymptotic covariance matrices are evaluated. Testing of hypotheses about the stationary distributions based on $\phi$--divergences between the estimated and empirical distributions is considered as well. Asymptotic distributions of $\phi$--divergence test statistics are found, enabling to specify asymptotically $\alpha$-level tests.