【摘要】 <正> 令（X,Y）为取值于 R^d×R 的随机向量,（X₁,Y₁）,……,（X_n,Y_n）为抽自（X,Y）的分布的 iid.样本,m（x）（?）E（Y|X=x）称为 Y 对 X 的回归函数.1964年,Watson和 Nadaraya 首先提出用更多还原

【Abstract】 Let（X_i,Y_i）,i=1,…,n,be R^d×R-valued i.i.d.samples taken from the distribution of（X,Y）.Denote the regression function by m（x）=E（Y|X=x）.In this paper,we consi-der the kernel estimators m_n（x）of m（x）based on （X₁,Y₁）,…,（X_n,Y_n）,which were in-troduced by Watson[1]and Nadaraya[2],but here the window size h_n is supposed tobe a sequence of positive random variables which depend on x and samples X₁,…,X_n.Weprove the uniform weak convergence of m_n（x）.This case has also been studied by Sch-uster and Yakowitz[3],who assumed that d=1 and h_n is a sequence of positive con-stants.更多还原