Geodesic
Inference about stationary distributions of Markov chains based on divergences with observed frequencies
Kybernetika, Tome 35 (1999) no. 3, pp. 265-280 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 62E20, 62M02, 62M05
Keywords: $\phi$-divergence; empirical distributions; parameter estimation; hypotheses testing 
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     author = {Men\'endez, Mar{\'\i}a Luisa and Morales, Domingo and Pardo, Leandro and Vajda, Igor},
     title = {Inference about stationary distributions of {Markov} chains based on divergences with observed frequencies},
     journal = {Kybernetika},
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Menéndez, María Luisa; Morales, Domingo; Pardo, Leandro; Vajda, Igor. Inference about stationary distributions of Markov chains based on divergences with observed frequencies. Kybernetika, Tome 35 (1999) no. 3, pp. 265-280. http://geodesic.mathdoc.fr/item/KYB_1999_35_3_a0/

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