Central limit theorem for integrated square error of kernel estimators of spherical density

被引：15
|
作者：
Zhao, LC [1 ]
Wu, CQ [1 ]
机构：
[1] Univ Sci & Technol China, Dept Stat & Finance, Hefei 230026, Peoples R China
来源：
SCIENCE IN CHINA SERIES A-MATHEMATICS PHYSICS ASTRONOMY | 2001年 / 44卷 / 04期
关键词：
central limit theorem; directional data; kernel estimate; integrated square error;
D O I：
10.1007/BF02881884
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let X,,,X, be lid observations of a random variable X with probability density function f(x) on the q-dimensional unit sphere Ohm (q), in Rq+1, q greater than or equal to 1. Let f(n)(x) = n(-1)c(h) Sigma K-n(i=1)[(1-x'X-i)/h(2)] be a kernel estimator of f(x). In this paper we establish a central limit theorem for integrated square error of f(n) under some mild conditions.
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页码：474 / 483
页数：10
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