回归函数及其导数非参数估计的强一致收敛速度  

Strong Uniform Convergence Rates for Nonparamatric Estimation of Conditional Function and Its Derivatives

作　　者：朱仲义[1] 韦博成[2] 

机构地区：[1]河海大学机械学院公共课部 [2]东南大学

出　　处：《河海大学机械学院学报》1997年第1期10-17,共8页

基　　金：国家自然科学基金;常州分校科研基金资助项目

摘　　要：本文研究了回归函数及其导数的非参数估计.对随机与固定设计的回归函数,分别利用核估计和非参数加权估计,在核函数及权函数满足一条件下,本文证明了估计一致强收敛于待估函数的速度可达到最优.从而进一步推广和发展了Hardle(1988)、Severini,etal.(1992)的许多结果.In this paper, the nonparametric estimation of conditional function and its derivatives are studied. Strong uniform convergence rates are proved to be optimal for kernel-type estimator and weighted estimator of conditional function in the fixed design and random design, under certain conditions. Various previous results in the literature (for example Hardel, etal. 1988,) (Severini and Wong 1992)) are extended and developed.

关 键 词：回归函数 强一致收敛 收敛速度 导数 非参数估计 

分 类 号：O212.7[理学—概率论与数理统计]