The Nadaraya–Watson kernel regression function estimator

Abstract

This chapter reviews the asymptotic properties of the Nadaraya-Watson type kernel estimator of an unknown (multivariate) regression function. Conditions are set forth for pointwise weak and strong consistency, asymptotic normality, and uniform consistency. These conditions cover the standard i.i.d. case with continuously distributed regressors, as well as the cases where the distribution of all, or some, regressors is discrete. Moreover, attention is paid to the problem of how the kernel and the window width should be specified. This chapter is a modified and extended version of Bierens (1987b). For further reading and references, see the monographs by Eubank (1988), Hardle (1990), and Rosenblatt (1991), and for an empirical application, see Bierens and Pott-Buter (1990).