Kybernetika 35 no. 3, 265-280, 1999

Inference about stationary distributions of Markov chains based on divergences with observed frequencies

María Luisa Menéndez, Domingo Morales, Leandro Pardo and Igor Vajda

Abstract:

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.