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Recursive estimation of the transition distribution function of a Markov process: A symptotic normality

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  • Roussas, George G.

Abstract

Let X1,..., Xn + 1 be the first n + 1 random variables from a strictly stationary Markov process which satisfies certain additional regularity conditions. On the basis of these random variables, a recursive nonparametric estimate of the one-step transition distribution function is shown to be asymptotically normal. The class of Markov processes studied includes the Markov processes usually considered in the literature; namely, processes which either satisfy Doeblin's hypothesis, or, more generally, are geometrically ergodic.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:11:y:1991:i:5:p:435-447
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    Cited by:

    1. De Gooijer, Jan G. & Gannoun, Ali & Zerom, Dawit, 2002. "Mean squared error properties of the kernel-based multi-stage median predictor for time series," Statistics & Probability Letters, Elsevier, vol. 56(1), pages 51-56, January.
    2. Schick, Anton & Wefelmeyer, Wolfgang, 2007. "Prediction in invertible linear processes," Statistics & Probability Letters, Elsevier, vol. 77(12), pages 1322-1331, July.
    3. Patrice Bertail & Stéphan Clémençon, 2005. "Regeneration-based Statistics for Harris Recurrent Markov Chains," Working Papers 2005-13, Center for Research in Economics and Statistics.

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