随机删失场合回归函数的核估计及强相合性  

KERNEL ESTIMATORS OF REGRESSION FUNCTION AND STRONG CONSISTENCY UNDER RANDOM CENSORSHIP

作　　者：陈平[1] 

机构地区：[1]东南大学数学力学系,南京210018

出　　处：《系统科学与数学》1992年第4期350-355,共6页Journal of Systems Science and Mathematical Sciences

基　　金：东南大学青年科学基金

摘　　要：回归函数的非参数估计及相合性问题曾经受到国内外学者的很大关注,但其中大多数都是基于完全样本来讨论的.如设(X_1,Y_1),…,(X_n,Y_n)是从 R^d×R 上的随机向量(X,Y)中抽取的 i.i.d.样本,陈希孺考虑了回归函数 m(x)=E(Y/X=x)的形如 m_n(x)=(?)W_(nj)(x)Y_i(其中 W_(nj)(x)为权函数)的非参数估计。Let(X_1, Y_1),…,(X_n,Y_n)be R^d×R-valued i.i.d.random vectors and {Yi} becensored by random variables {T_i}.It means that we can not observe Y_i butZ_i=min(Y_i,T_i) and δ_i=I(Y_i≤T_i),i=1, 2,…,n instead.Suppose that {Y(?)}is the class estimators of {Y_i}.In this paper,we first consider the three kernelestimators of m(x)=E(Y/X=x) and then prove the almost sure convergence ofthe kernel estimators under very weak conditions on kernel and window size.

关 键 词：回归函数 核估计 强相合性 

分 类 号：O212.1[理学—概率论与数理统计]