Roussas, George G. Recursive estimation of the transition distribution function of a Markov process: Asymptotic normality. (English) Zbl 0735.62082 Stat. Probab. Lett. 11, No. 5, 435-447 (1991). 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 Cited in 6 Documents MSC: 62M05 Markov processes: estimation; hidden Markov models 62E20 Asymptotic distribution theory in statistics 62G05 Nonparametric estimation Keywords:asymptotic normality; rho mixing; strictly stationary Markov process; recursive kernel-based nonparametric estimator; one-step transition distribution; Doeblin’s hypothesis; geometrically ergodic PDFBibTeX XMLCite \textit{G. G. Roussas}, Stat. Probab. Lett. 11, No. 5, 435--447 (1991; Zbl 0735.62082) Full Text: DOI References: [1] Loève, M., Probability Theory (1963), Van Nostrand: Van Nostrand Princeton, NJ · Zbl 0108.14202 [2] Masry, E., Nonparametric estimation of conditional probability densities and expectations of stochastic processes: Strong consistency and rates, Stochastic Process. Appl., 32, 109-127 (1989) · Zbl 0692.62034 [3] Roussas, G. G., Estimation of transition distribution function and its quantiles in Markov processes: Strong consistency and asymptotic normality, (Roussas, G. G., Nonparametric Functional Estimation and Related Topics (1991), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht) · Zbl 0735.62081 [4] Roussas, G. G.; Tran, L. T., Asymptotic normality of recursive kernel regression estimate under dependence conditions, (Tech. Rept. No. 187 (1989), Div. of Statist., Univ. of California: Div. of Statist., Univ. of California Davis, CA) · Zbl 0925.62171 [5] Roussas, G. G.; Tran, L. T., Joint asymptotic normality of kernel estimates under dependence, with applications to hazard rate, (Tech. Rept. No. 189 (1990), Div. of Statist., Univ. of California: Div. of Statist., Univ. of California Davis, CA) · Zbl 1360.62137 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.