LOCAL BANDWIDTH SELECTION FOR KERNEL DENSITY ESTIMATION IN BIFURCATING MARKOV CHAIN MODEL
| Autor: | Bitseki Penda , Siméon Valère, Roche , Angelina |
|---|---|
| Přispěvatelé: | Institut de Mathématiques de Bourgogne [Dijon] ( IMB ), Université de Bourgogne ( UB ) -Centre National de la Recherche Scientifique ( CNRS ), CEntre de REcherches en MAthématiques de la DEcision ( CEREMADE ), Université Paris-Dauphine-Centre National de la Recherche Scientifique ( CNRS ), Institut de Mathématiques de Bourgogne [Dijon] (IMB), Centre National de la Recherche Scientifique (CNRS)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université de Bourgogne (UB), CEntre de REcherches en MAthématiques de la DEcision (CEREMADE), Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL) |
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
60J80
Probability (math.PR) Nonparametric kernel estimation Mathematics - Statistics Theory Statistics Theory (math.ST) [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH] Bandwidth selection Binary trees 92D25 Bifurcating autoregressive process [ STAT.TH ] Statistics [stat]/Statistics Theory [stat.TH] [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] Mathematics Subject Classification (2010): 62G05 62G10 62G20 60J80 60F05 60F10 60J20 92D25 Bifurcating Markov chains 60F05 FOS: Mathematics 60J20 [ MATH.MATH-PR ] Mathematics [math]/Probability [math.PR] Mathematics - Probability 62G20 62G10 60F10 |
| Popis: | 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. 18 pages, 2 figures |
| Databáze: | OpenAIRE |
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