HAL: hal-00622861, version 2

arXiv: 1109.2694

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v1 (2011-09-13)

v2 (2012-02-28)

v3 (2012-06-22)

Kernel density estimation for stationary random fields

Mohamed El Machkouri 1

(2012-02-28)

In this paper, under natural and easily verifiable conditions, we prove the $\mathbb{L}^1$-convergence and the asymptotic normality of the Parzen-Rosenblatt density estimator for stationary 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 real random variables and $g$ is a measurable function defined on $\R^{\Z^d}$. Such kind of processes provides a general framework for stationary ergodic random fields. A Berry-Esseen's type central limit theorem is also given for the considered estimator.

1:	Laboratoire de Mathématiques Raphaël Salem (LMRS)
	CNRS : UMR6085 – Université de Rouen

Subject

:

Mathematics/Statistics Statistics/Statistics Theory

Keyword(s): Central limit theorem – spatial processes – m-dependent random fields – physical dependence measure – nonparametric estimation – kernel – density – rate of convergence

hal-00622861, version 2

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From: Mohamed EL MACHKOURI <>

Submitted on: Tuesday, 28 February 2012 11:23:35

Updated on: Tuesday, 28 February 2012 15:13:36