219 articles – 190 references  [version française]
 HAL: hal-00622861, version 2
 arXiv: 1109.2694
 Available versions: v1 (2011-09-13) v2 (2012-02-28) v3 (2012-06-22)
 Kernel density estimation for stationary random fields
 (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/StatisticsStatistics/Statistics Theory
 Keyword(s): Central limit theorem – spatial processes – m-dependent random fields – physical dependence measure – nonparametric estimation – kernel – density – rate of convergence
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 hal-00622861, version 2 http://hal.archives-ouvertes.fr/hal-00622861 oai:hal.archives-ouvertes.fr:hal-00622861 From: Mohamed EL MACHKOURI <> Submitted on: Tuesday, 28 February 2012 11:23:35 Updated on: Tuesday, 28 February 2012 15:13:36