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

2017/06/21 by S. Valère Bitseki Penda, Penda, S Valere Bitseki, Angelina Roche +1 · 1 citation
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1706.07034

openalex publication_date 2017/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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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