Kernel density estimation for stationary random fields

الأصل · EN

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 ∈ ᵈ), k∈ᵈ, where (εᵢ)ᵢ∈ᵈ are i.i.d real random variables and g is a measurable function defined on 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.