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Recursive estimation of the transition distribution function of a Markov process: Asymptotic normality. (English) Zbl 0735.62082

Consider a strictly stationary Markov process \(X_ 1,X_ 2,\ldots.\) A recursive kernel-based nonparametric estimator of the one-step transition distribution is shown to be asymptotically normal, under stated regularity conditions. The class of Markov processes satisfying these conditions includes the Markov processes usually considered in the literature; namely, processes which either satisfy Doeblin’s hypothesis, or, more generally, are geometrically ergodic.
[Editorial remark: See also the author’s article reviewed above.].
Reviewer: B.H.Lindqvist

MSC:

62M05 Markov processes: estimation; hidden Markov models
62E20 Asymptotic distribution theory in statistics
62G05 Nonparametric estimation
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References:

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