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Large deviations of kernel density estimator in L1(Rd) for uniformly ergodic Markov processes

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  • Lei, Liangzhen
  • Wu, Liming

Abstract

In this paper, we consider a uniformly ergodic Markov process (Xn)n[greater-or-equal, slanted]0 valued in a measurable subset E of Rd with the unique invariant measure , where the density f is unknown. We establish the large deviation estimations for the nonparametric kernel density estimator in L1(Rd,dx) and for , and the asymptotic optimality in the Bahadur sense. These generalize the known results in the i.i.d. case.

Suggested Citation

  • Lei, Liangzhen & Wu, Liming, 2005. "Large deviations of kernel density estimator in L1(Rd) for uniformly ergodic Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 115(2), pages 275-298, February.
    • Handle: RePEc:eee:spapps:v:115:y:2005:i:2:p:275-298
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    References listed on IDEAS

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    1. Bosq, Denis & Merlevède, Florence & Peligrad, Magda, 1999. "Asymptotic Normality for Density Kernel Estimators in Discrete and Continuous Time," Journal of Multivariate Analysis, Elsevier, vol. 68(1), pages 78-95, January.
    2. Carrasco, Marine & Chen, Xiaohong, 2002. "Mixing And Moment Properties Of Various Garch And Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 18(1), pages 17-39, February.
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    Cited by:

    1. Gao, Fuqing, 2008. "Moderate deviations and law of the iterated logarithm in for kernel density estimators," Stochastic Processes and their Applications, Elsevier, vol. 118(3), pages 452-473, March.

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