Kernel deconvolution estimation for random fields

Ahmed El Ghini (1) , Mohamed El Machkouri (2)

1 UM5 - Université Mohammed V de Rabat [Agdal]
2 LMRS - Laboratoire de Mathématiques Raphaël Salem

In this work, we establish the asymptotic normality of the deconvolution kernel density estimator in the context of strongly mixing random fields. Only minimal conditions on the bandwidth parameter are required and a simple criterion on the strong mixing coefficients is provided. Our approach is based on the Lindeberg's method rather than on Bernstein's technique and coupling arguments widely used in previous works on nonparametric estimation for spatial processes. We deal also with nonmixing random fields which can be written as a (nonlinear) functional of i.i.d. random fields by considering the physical dependence measure coefficients introduced by Wu (2005).

Mots clés: physical dependence measure; Central limit theorem; deconvolution kernel density estimator; strongly mixing random fields; nonmixing random fields; physical dependence measure.

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

Ahmed El Ghini, Mohamed El Machkouri. Kernel deconvolution estimation for random fields. 2011. ⟨hal-00655770⟩