方向数据密度核估计的对数律  

A Law of the Logarithm for Kernel Density Estimator with Directional Data

作　　者：王小明[1] 赵林城[1] 

机构地区：[1]中国科技大学统计与金融系,合肥230026

出　　处：《数学学报（中文版）》2003年第5期865-874,共10页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金(19631040;19971085);国家教委博士点基金

摘　　要：设X为取值于k维单位球面上的单位随机向量,具有概率密度函数f(x),X_1,…,X_n为X的n个i.i.d.的观察,讨论f(x)具有形式的核估计,其中K为定义于[0,+∞]上的非负核函数,ω_k为Ω_k上的Lebesque测度,本文建立了fn(x)的对数律,并给出了fn(x)的一致强相合速度。Let X be a random vector taking values on a k-dimensional unit sphere with probability density function (p.d.f.) /(x), and X1,...,Xn be a list of independent and identically distributed (i.i.d.) observations from X. The kernel estimator of f(x) considered here is of the form fn(x) = . where K is a kernel function defined on [0,+∞), ωk is the Lebesgue measure on Ωk. In this paper, we establish the uniformly strong consistency rates of fn(x) by deriving a law of the Logarithm for it.

关 键 词：方向数据 密度函数 核估计 对数律 

分 类 号：O211.7[理学—概率论与数理统计]