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

Bitseki Penda, Siméon Valère; Roche, Angelina (2020), Local bandwidth selection for kernel density estimation in a bifurcating Markov chain model, Journal of Nonparametric Statistics, 32, 3, p. 535-562. 10.1080/10485252.2020.1789125

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Type
Article accepté pour publication ou publié
Date
2020
Nom de la revue
Journal of Nonparametric Statistics
Volume
32
Numéro
3
Éditeur
Taylor & Francis
Pages
535-562
Identifiant publication
Métadonnées
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Auteur(s)
Bitseki Penda, Siméon Valère
Institut de Mathématiques de Bourgogne [Dijon] [IMB]
Roche, Angelina
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Résumé (EN)
We propose an adaptive estimator for the stationary distribution of a bifurcating Markov Chain onRd. 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 Statistics3: 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.
Mots-clés
Nonparametric kernel estimation; Goldenshluger-Lepski methodology; adaptive estimation; binary trees; bifurcating autoregressive processes