Asymptotic normality of kernel estimates in a regression model for random fields

Key words : Asymptotic normality, Ballistic random walk, Confidence regions, Cramér-Rao efficiency, Maximum likelihood estimation, Random walk in ran- dom environment.. MSC 2000

We suggest a nonparametric regression estimation approach which is to aggregate over space.That is, we are mainly concerned with kernel regression methods for functional random

For a review and a large list of references, we refer the reader to Ba´ıllo, Cuevas, and Jus- tel (2000), Biau, Cadre, and Pelletier (2008) and Mason and Polonik (2009).. Devroye

Keywords: Kernel estimator; Spatial regression; Random fields; Strong mixing coef- ficient; Dimension reduction; Inverse Regression.. The set S can be discret, continuous or the set

One can recall the works of [33], based on a maximum likelihood approach in the Hall class of distribution functions (see [18]), [7] who use a fixed number of nonparametric

Key words and phrases: Central limit theorem, spatial processes, m-dependent random fields, physical dependence measure, nonparametric estimation, kernel density estimator, rate

Key words and phrases: Central limit theorem, spatial processes, random fields, nonparametric density estimation, frequency polygon, histogram, mixing.. 1 Introduction

Key words and phrases: Central limit theorem, deconvolution kernel density esti- mator, strongly mixing random fields, nonmixing random fields, physical depen- dence measure..