非参数回归函数的随机窗宽核估计的重对数律

设(X,Y),(X_1,Y_1),(X_2,Y_2),…为 i.i.d.二维随机变量序列,具有联合分布F(x,y)及密度 f(x,y).X 的边际分布和密度分别记为 F_X(x)和 f_X(x).记 m(x)=E{Y|X=x)}为 Y 对 X 的回归函数.为估计 m(x),Nadaraya 和 watson 独立地引进了如下形式的核估计

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

In this paper we study the estimation of the regression function.We estabilish a law ofthe iterated logarithm for the random window-width kernel estimator and,as an applicationfor a kind of nearest neighbor estimator.These results give sharp pointwise rates of strongconsitency of these estimators.