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

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.

arXiv comment18 pages, 2 figures

References in corpus (4)

• Data-driven calibration of penalties for least-squares regression
• Limit theorems for bifurcating Markov chains. Application to the detection of cellular aging
• Deviation inequalities, Moderate deviations and some limit theorems for bifurcating Markov chains with application
• Adaptation to lowest density regions with application to support recovery