Pré-Publication, Document De Travail Année : 2012

Kernel density estimation for stationary random fields

Résumé

In this paper, under natural and easily verifiable conditions, we prove the L1-convergence and the asymptotic normality of the Parzen-Rosenblatt density estimator for stationary random fields of the form Xk=g(εks,s\Zd), k\Zd, where (εi)i\Zd are i.i.d real random variables and g is a measurable function defined on \R\Zd. 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.
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Dates et versions

hal-00622861 , version 1 (12-09-2011)
hal-00622861 , version 2 (28-02-2012)
hal-00622861 , version 3 (21-06-2012)
hal-00622861 , version 4 (26-07-2013)
hal-00622861 , version 5 (01-05-2014)

Identifiants

Citer

Mohamed El Machkouri. Kernel density estimation for stationary random fields. 2012. ⟨hal-00622861v2⟩
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