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Regeneration-based Statistics for Harris Recurrent Markov Chains

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  • Patrice Bertail

    (Crest)

  • Stéphan Clémençon

    (Crest)

Abstract

In this paper an attempt is made to present how renewalproperties of Harris recurrent Markov chains or of specific extensions of thelatter may be practically used for statistical inference in various settings.In the regenerative case, procedures can be implemented from data blockscorresponding to consecutive observed regeneration times for the chain. Themain idea for extending the application of these statistical techniques to generalHarris chains X consists in generating first a sequence of approximaterenewal times for a regenerative extension of X from data X1; :::; Xn and theparameters of a minorization condition satisfied by its transition probabilitykernel. Numerous applications of this estimation principle may be consideredin both the stationary and nonstationary (including the null recurrentcase) frameworks. This article deals with some important procedures basedon (approximate) regeneration data blocks, from both practical and theoreticalviewpoints, for the following topics: mean and variance estimation,confidence intervals, U-statis

Suggested Citation

  • Patrice Bertail & Stéphan Clémençon, 2005. "Regeneration-based Statistics for Harris Recurrent Markov Chains," Working Papers 2005-13, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2005-13
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    References listed on IDEAS

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    1. George Roussas, 1969. "Nonparametric estimation in Markov processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 21(1), pages 73-87, December.
    2. J. Michael Harrison & Sidney I. Resnick, 1976. "The Stationary Distribution and First Exit Probabilities of a Storage Process with General Release Rule," Mathematics of Operations Research, INFORMS, vol. 1(4), pages 347-358, November.
    3. Müller, Ursula U. & Schick, Anton & Wefelmeyer, Wolfgang, 2001. "Improved estimators for constrained Markov chain models," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 427-435, October.
    4. Roussas, George G., 1991. "Recursive estimation of the transition distribution function of a Markov process: A symptotic normality," Statistics & Probability Letters, Elsevier, vol. 11(5), pages 435-447, May.
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