Large Deviations and Moderate Deviations for Kernel Density Estimators of Directional Data  

作　　者：Fu Qing GAO Li Na LI 

机构地区：[1]School of Mathematics and Statistics, Wuhan University, Wuhan 430072, P. R. China [2]Department of Mathematics, Tongji University, Shanghai 200092, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2010年第5期937-950,共14页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China (Grant No. 10571139)

摘　　要：Let fn be the non-parametric kernel density estimator of directional data based on a kernel function K and a sequence of independent and identically distributed random variables taking values in d-dimensional unit sphere Sd-1. It is proved that if the kernel function is a function with bounded variation and the density function f of the random variables is continuous, then large deviation principle and moderate deviation principle for {sup x∈sd-1 ｜fn（x） - E（fn（x））｜, n ≥ 1} hold.Let fn be the non-parametric kernel density estimator of directional data based on a kernel function K and a sequence of independent and identically distributed random variables taking values in d-dimensional unit sphere Sd-1. It is proved that if the kernel function is a function with bounded variation and the density function f of the random variables is continuous, then large deviation principle and moderate deviation principle for {sup x∈sd-1 ｜fn（x） - E（fn（x））｜, n ≥ 1} hold.

关 键 词：kernel density estimator directional data moderate deviations large deviations 

分 类 号：O211.4[理学—概率论与数理统计] S792.17[理学—数学]