随机窗宽下经验若当变换的收敛速度  

RATE OF CONVERGENCE OF THE EMPIRICAL RADON TRANSFORM FOR RANDOM WINDOW-BANDWIDTH

作　　者：崔恒建[1] 

机构地区：[1]北京师范大学数学系

出　　处：《北京师范大学学报（自然科学版）》1996年第3期285-288,共4页Journal of Beijing Normal University(Natural Science)

基　　金：国家自然科学基金;博士后基金

摘　　要：给出了随机窗宽下的核型经验若当变换，在一空条件下，获得了此经验若当变换中心在原点的一致精确强收敛速度以及对中心也一致的一致强收敛速度，所得结果与最优性与非随机窗宽下的核型经验若当变换一致，并以近邻核型经验若当变换为典型实例。Motivated by recent works of Gilliam et al on exploratory projection pursuit,the empirical Radon transfoum for random window-bandwidth is defined. Its precise convergence rate at a fixed centre, uniform over all orientations, and its precise convergence rate uniformly over all centres and all orientations are derived. It is shown that in the sense of optimizing the uniform convergence rate, and as an application for a kind of nearest neighbor estimator.

关 键 词：经验若当变换 随机窗宽 估计 收敛速度 若当变换 

分 类 号：O211.67[理学—概率论与数理统计]