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(εk−s,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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