Kernel density estimation for stationary random fields

Mohamed El Machkouri (1)

1 LMRS - Laboratoire de Mathématiques Raphaël Salem

This paper establishes the asymptotic normality of the Parzen-Rosenblatt density estimator for stationary random fields under natural and easily verifiable conditions. We deal with random fields of the form $X_k = g\left(\varepsilon_{k-s}, s \in \Z^d \right)$, $k\in\Z^d$, where $(\varepsilon_i)_{i\in\Z^d}$ are i.i.d random variables and $g$ is a measurable function. Such kind of spatial processes provides a general framework for stationary ergodic random fields. In particular, in the one-dimensional case, this class of processes includes linear as well as many widely used nonlinear time series models as special cases.

Mots clés: Central limit theorem; spatial processes; m-dependent random fields; physical dependence measure; nonparametric estimation; kernel; density

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

Mohamed El Machkouri. Kernel density estimation for stationary random fields. 2011. ⟨hal-00622861v1⟩