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Nonparametric estimation of conditional probability densities and expectations of stationary processes: strong consistency and rates

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  • Masry, Elias

Abstract

Let {Xj} [infinity]j=-[infinity] be a real-valued stationary process. Recursive kernel estimators of the joint probability density functions, of conditional probability densities, and of the conditional expectations of functionals of Xj, given past behavior, are considered. Their strong consistency, along with rates, are established for processes {Xj} satisfying various mixing conditions.

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  • Masry, Elias, 1989. "Nonparametric estimation of conditional probability densities and expectations of stationary processes: strong consistency and rates," Stochastic Processes and their Applications, Elsevier, vol. 32(1), pages 109-127, June.
    • Handle: RePEc:eee:spapps:v:32:y:1989:i:1:p:109-127
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    Cited by:

    1. P. Cattiaux & José R. León & C. Prieur, 2015. "Recursive estimation for stochastic damping hamiltonian systems," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 27(3), pages 401-424, September.
    2. Schick, Anton & Wefelmeyer, Wolfgang, 2007. "Prediction in invertible linear processes," Statistics & Probability Letters, Elsevier, vol. 77(12), pages 1322-1331, July.
    3. Masry, Elias, 2002. "Multivariate probability density estimation for associated processes: strong consistency and rates," Statistics & Probability Letters, Elsevier, vol. 58(2), pages 205-219, June.

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