We review diﬀerent approaches to nonparametric density and regression estimation. Kernel estimators are motivated from local averaging and solving ill-posed problems. Kernel estimators are compared to k-NN estimators, orthogonal series and splines. Pointwise and uniform conﬁdence bands are described, and the choice of smoothing parameter is discussed. Finally, the method is applied to nonparametric prediction of time series and to semiparametric estimation.
Published in D. F. McFadden and R. F. Engle, eds., The Handbook of Econometrics, Vol. IV, North Holland, 1994, pp. 2295-2339 [DOI]