LOCAL BANDWIDTH SELECTION FOR KERNEL DENSITY ESTIMATION IN BIFURCATING MARKOV CHAIN MODEL

Siméon Valère Bitseki Penda (1) , Angelina Roche (2)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

We propose an adaptive estimator for the stationary distribution of a bifurcating Markov Chain on 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.

Mots clés: Bandwidth selection; Bifurcating autoregressive process; Bifurcating Markov chains; Binary trees; Nonparametric kernel estimation; 62G10; 62G20; 60J80; 60F05; 60F10; 60J20; 92D25

Domaines: Théorie [stat.TH]; Probabilités [math.PR]

Siméon Valère Bitseki Penda, Angelina Roche. LOCAL BANDWIDTH SELECTION FOR KERNEL DENSITY ESTIMATION IN BIFURCATING MARKOV CHAIN MODEL. 2017. ⟨hal-01557228⟩