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Statistical inference for finite Markov chains based on divergences

Author

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  • Menéndez, M. L.
  • Morales, D.
  • Pardo, L.
  • Zografos, K.

Abstract

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 them. The inference is based on statistics which are suitable weighted sums of normed [phi]-divergences of theoretical row distributions, evaluated at suitable points, and observed empirical row distributions. The asymptotic distribution of minimum [phi]-divergence estimators is obtained, as well as critical values of asymptotically [alpha]-level tests.

Suggested Citation

  • Menéndez, M. L. & Morales, D. & Pardo, L. & Zografos, K., 1999. "Statistical inference for finite Markov chains based on divergences," Statistics & Probability Letters, Elsevier, vol. 41(1), pages 9-17, January.
    • Handle: RePEc:eee:stapro:v:41:y:1999:i:1:p:9-17
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    References listed on IDEAS

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    1. Salicru, M. & Morales, D. & Menendez, M. L. & Pardo, L., 1994. "On the Applications of Divergence Type Measures in Testing Statistical Hypotheses," Journal of Multivariate Analysis, Elsevier, vol. 51(2), pages 372-391, November.
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    Cited by:

    1. Abhik Ghosh, 2022. "Robust parametric inference for finite Markov chains," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(1), pages 118-147, March.
    2. R. Jiménez & J. E. Yukich, 2002. "Asymptotics for Statistical Distances Based on Voronoi Tessellations," Journal of Theoretical Probability, Springer, vol. 15(2), pages 503-541, April.
    3. M. Menéndez & J. Pardo & L. Pardo, 2001. "Csiszar’s ϕ-divergences for testing the order in a Markov chain," Statistical Papers, Springer, vol. 42(3), pages 313-328, July.

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