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

S Valere Bitseki Penda; Angelina Roche

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arXiv · 1706.07034

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

S Valere Bitseki Penda·Angelina Roche

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Abstract

We propose an adaptive estimator for the stationary distribution of a bifurcating Markov Chain on $\mathbb R^d$. Bifurcating Markov chains (BMC for short) are a class of stochastic processes indexed by regular binary trees. A kernel estimator is proposed whose bandwidth is selected by a method inspired by the works of Goldenshluger and Lepski [18]. Drawing inspiration from dimension jump methods for model selection, we also provide an algorithm to select the best constant in the penalty.

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S Valere Bitseki Penda, Angelina Roche. 2017-06-21. Local bandwidth selection for kernel density estimation in bifurcating Markov chain model. https://arxiv.org/abs/1706.07034

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