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Local bandwidth selection for kernel density estimation in a bifurcating Markov chain model

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  • S. Valère Bitseki Penda
  • Angelina Roche

Abstract

We propose an adaptive estimator for the stationary distribution of a bifurcating Markov Chain on $\mathbb R^d $Rd. Bifurcating Markov chains (BMC for short) are a class of stochastic processes indexed by regular binary trees. A kernel estimator is proposed whose bandwidths are selected by a method inspired by the works of Goldenshluger and Lepski [(2011), ‘Bandwidth Selection in Kernel Density Estimation: Oracle Inequalities and Adaptive Minimax Optimality’, The Annals of Statistics 3: 1608–1632). Drawing inspiration from dimension jump methods for model selection, we also provide an algorithm to select the best constant in the penalty. Finally, we investigate the performance of the method by simulation studies and application to real data.

Suggested Citation

  • S. Valère Bitseki Penda & Angelina Roche, 2020. "Local bandwidth selection for kernel density estimation in a bifurcating Markov chain model," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 32(3), pages 535-562, July.
    • Handle: RePEc:taf:gnstxx:v:32:y:2020:i:3:p:535-562
    DOI: 10.1080/10485252.2020.1789125
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    Cited by:

    1. Bitseki Penda, S. Valère, 2023. "Moderate deviation principles for kernel estimator of invariant density in bifurcating Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 158(C), pages 282-314.
    2. S. Valère Bitseki Penda & Jean-François Delmas, 2023. "Central Limit Theorem for Kernel Estimator of Invariant Density in Bifurcating Markov Chains Models," Journal of Theoretical Probability, Springer, vol. 36(3), pages 1591-1625, September.

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