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Comparative Construction of Plug-in Estimators of the Entropy Rate of Two-state Markov Chains

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  • Valérie Girardin

    (Université de Caen)

  • André Sesboüé

    (Université de Caen)

Abstract

The entropy rate of an ergodic homogeneous Markov chain taking only two values is an explicit function of its transition probabilities. We study plug-in estimators of this entropy rate based on the observation of either one trajectory with long length or several trajectories with fixed length. Their exact asymptotic distributions are given. A detailed numerical study using simulation results is provided. Real data of rainfall occurrences are studied.

Suggested Citation

  • Valérie Girardin & André Sesboüé, 2009. "Comparative Construction of Plug-in Estimators of the Entropy Rate of Two-state Markov Chains," Methodology and Computing in Applied Probability, Springer, vol. 11(2), pages 181-200, June.
    • Handle: RePEc:spr:metcap:v:11:y:2009:i:2:d:10.1007_s11009-008-9106-2
    DOI: 10.1007/s11009-008-9106-2
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    References listed on IDEAS

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    1. Bisgaard, Søren & Travis, Laurel E., 1991. "Existence and uniqueness of the solution of the likelihood equations for binary Markov chains," Statistics & Probability Letters, Elsevier, vol. 12(1), pages 29-35, July.
    2. Valerie Girardin, 2004. "Entropy Maximization for Markov and Semi-Markov Processes," Methodology and Computing in Applied Probability, Springer, vol. 6(1), pages 109-127, March.
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    Cited by:

    1. Guglielmo D’Amico, 2015. "Rate of Occurrence of Failures (ROCOF) of Higher-Order for Markov Processes: Analysis, Inference and Application to Financial Credit Ratings," Methodology and Computing in Applied Probability, Springer, vol. 17(4), pages 929-949, December.

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