摘要
本文提出了利用一维核函数构造多维密度函数一个新估计的方法.首先利用球极投影变换将具有密度f(x),X∈Rd的样本变换为具有密度g(y),y∈Ωd+1={y:y∈Rd+1,‖y‖=1)的样本.其次,建立f与g的关系.最后,利用球面数据密度核估计构造f的一个新估计f^n.在核K及密度f(x)满足一定条件(见§1定理1.1)下,获得了f^n到,的逐点强收敛速度.
In this paper, a new kernel estimator of multivariate density is proposed by using a univariate kernel function. The main idea is that firstly transform the sample from the multivariate density f(x), x∈Rd to a sample from the density g(y), y∈Ωd+1 ={y: y∈Rd+1, ‖y‖= 1}, which is dependent on f(·) by stereographic projection transformation and secondly construct kernel density estimator f^n(x) by using the results of kernel density estimator with spherical data. The authors also get some results on convergence rate of f^n(x) to f(x) under the assumption of kernel K and density function f(x) (see Theorem 1.1 in Section 1).
出处
《数学年刊（A辑）》
CSCD
北大核心
2005年第1期19-30,共12页
Chinese Annals of Mathematics
基金
国家自然科学基金(No.10371005)资助的项目.
关键词
核密度估计
球极投影变换
球面数据
收敛速度
Kernel density estimator, Stereographic projection transformation, Spherical data, Convergence rate
