A LAW OF THE ITERATED LOGARITHM FOR RANDOM WINDOW-WIDTH KERNEL ESTIMATOR OF A NONPARAMETRIC REGRESSION FUNCTION

摘要

In this paper we study the estimation of the regression function.We establish a law ofthe iterated logarithm for the random window-width kernel estimator and,as an application,fora nearest neighbor estimator.These results give sharp pointwise rates of strong consistency ofthese estimators.