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$\phi$-divergence; empirical distributions; parameter estimation; hypotheses testing
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.
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