随机删失场合基于Synthetic Data的回归函数的核估计及强相合性  

Regression Function Kernel Estimation Based on Synthetic Data Under Random Censorship

作　　者：卢学文[1] 

机构地区：[1]湖南师范大学,长沙410081

出　　处：《应用概率统计》1996年第1期29-36,共8页Chinese Journal of Applied Probability and Statistics

基　　金：国家自然科学基金资助项目;高校博士学科点专项科研基金资助项目

摘　　要：设(X_1,Y_1),…,(X_n,Y_n)是来自总体(X,Y)的取值于R^d×R上的i.i.d.随机向量,是未知的非参数回归函数,{Y_i}被随机变量{T_i}删失,只能观察到,本文分别在T_i的分布函数已知和未知的情形下,利用Leurgans等人提出的Synthetic data方法获得新的数据{Y_i~*}与{Y_i^(**)},考虑了m(x)的核估计并且证明了其强相合性。Let (X1, Y1), …, (Xn, Yn) be i.i.d. Rd × R random vectors coming from population (X, Y), and m(x) = E(Y|X = x) be a unknown nonparametric regression function. Now, {Yi} are randomly censored by {Ti} , where {Ti} are i.i.d. samples of random variable T, independent of {(Xi, Yi)}. We can only observe Zt = min{Yi, Ti}, δi= [Yi ≤ Ti], i = 1, ???, n. When T's distribution function is known and unknown, respectively, this paper obtains new data {Yi*} and {Vi**} using the synthetic data method proposed by Leurgans, etc., and proposes the kernel estimates M*(x) and m**(x) of m(x), under some conditions, these estimates are shown strongly consistent.

关 键 词：非参数回归 估计估计 强相合性 合成数据法 

分 类 号：O212.7[理学—概率论与数理统计]