Asymptotic normality of the Parzen-Rosenblatt density estimator for strongly mixing random fields

Mohamed El Machkouri (1)

1 LMRS - Laboratoire de Mathématiques Raphaël Salem

We prove the asymptotic normality of the kernel density estimator (introduced by Rosenblatt (1956) and Parzen (1962)) in the context of stationary strongly mixing random fields. Our approach is based on the Lindeberg's method rather than on Bernstein's small-block-large-block technique and coupling arguments widely used in previous works on nonparametric estimation for spatial processes. Our method allows us to consider only minimal conditions on the bandwidth parameter and provides a simple criterion on the strong mixing coefficients which do not depend on the bandwith.

Mots clés: Central limit theorem; Kernel density estimator; Strongly mixing random fields; Spatial processes

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

Mohamed El Machkouri. Asymptotic normality of the Parzen-Rosenblatt density estimator for strongly mixing random fields. 2010. ⟨hal-00530145⟩