Approximation for general bootstrap of empirical processes with an application to kernel-type density estimation

Salim Bouzebda (1) , Omar El-Dakkak (1)

1 LSTA - Laboratoire de Statistique Théorique et Appliquée

The purpose of this note is to provide an approximation for the generalized bootstrapped empirical process achieving the rate in Kolmos et al. (1975). The proof is based on much the same arguments as in Horvath et al. (2000). As a consequence, we establish an approximation of the bootstrapped kernel-type density estimator

Mots clés: General bootstrap; Brownian bridge; Best approximation; kernel density estimator

Domaines: Théorie [stat.TH]; Statistiques [math.ST]

Salim Bouzebda, Omar El-Dakkak. Approximation for general bootstrap of empirical processes with an application to kernel-type density estimation. 2009. ⟨hal-00371340⟩