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On kernel estimators of density for reversible Markov chains

Author

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  • Longla, Martial
  • Peligrad, Magda
  • Sang, Hailin

Abstract

In this paper we investigate the kernel estimator of the density for a stationary reversible Markov chain. The proofs are based on a new central limit theorem for a triangular array of reversible Markov chains obtained under conditions imposed to covariances, which has interest in itself.

Suggested Citation

  • Longla, Martial & Peligrad, Magda & Sang, Hailin, 2015. "On kernel estimators of density for reversible Markov chains," Statistics & Probability Letters, Elsevier, vol. 100(C), pages 149-157.
    • Handle: RePEc:eee:stapro:v:100:y:2015:i:c:p:149-157
    DOI: 10.1016/j.spl.2015.02.013
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    References listed on IDEAS

    as
    1. Liebscher, Eckhard, 1999. "Asymptotic normality of nonparametric estimators under [alpha]-mixing condition," Statistics & Probability Letters, Elsevier, vol. 43(3), pages 243-250, July.
    2. Wu, Wei Biao & Huang, Yinxiao & Huang, Yibi, 2010. "Kernel estimation for time series: An asymptotic theory," Stochastic Processes and their Applications, Elsevier, vol. 120(12), pages 2412-2431, December.
    3. 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.
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