On a class of recursive estimators for spatially dependent observations

Abstract

We investigate the mean squared error and the asymptotic normality for a class of recursive kernel estimators based on a sample of spatially dependent observations. Our main result provides sufficient conditions for a spatial version of a recursive estimator introduced by Hall and Patil (1994) to satisfy a central limit theorem. The results are stated for strongly mixing random fields in the sense of Rosenblatt (1956) and for weakly dependent random fields in the sense of Wu (2005).