A Note on Asymptotic Normality of Kernel Estimation for Linear Random Fields on Z 2

Abstract

This note considers the kernel estimation of a linear random field on Z2. Instead of imposing certain mixing conditions on the random fields, it is assumed that the weights of the innovations satisfy a summability property. By building a martingale decomposition based on a suitable filtration, asymptotic normality is proven for the kernel estimator of the marginal density of the random field.