条件泛函及其导数非参数估计的强一致收敛速度  

Strong Uniform Convergence Rates for Nonparametric Estimations of Conditional Functional and its Derivatives

作　　者：朱仲义[1] 韦博成[1] 

机构地区：[1]东南大学数力系,南京210096

出　　处：《数学物理学报（A辑）》1998年第4期394-401,共8页Acta Mathematica Scientia

基　　金：国家自然科学基金;江苏省自然科学基金资助项目

摘　　要：研究了条件泛函及其导数的非参数估计,对随机与固定设计的条件泛函,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定条件下,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Hrdle,etal.(1988)、Severini,etal.(1992)的许多结果。In this paper, the nonparameteric estimations of conditional functional and its derivatives are studied. Strong uniform convergence rates are proved to be optimal for kernel type estimator and weighted estimator of conditional functional in the random design and the fixed design,under certain conditions. Various previous results in the literature (for example Hardle etal. (1988) .Severini and Wong (1992) are extended and sharpened.

关 键 词：条件泛函 导数 非参数估计 强一致收敛速度 

分 类 号：O212.7[理学—概率论与数理统计]