On the Nadaraya–Watson kernel regression estimator for irregularly spaced spatial data

Abstract

We investigate the asymptotic normality of the Nadaraya–Watson kernel regression estimator for irregularly spaced data collected on a finite region of the lattice Zd where d is a positive integer. 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). Only minimal conditions on the bandwidth parameter and simple conditions on the dependence structure of the data are assumed.