Non-uniform Randomized Sampling for Multivariate Approximation by High Order Parzen Windows

被引：5

作者：

Zhou, Xiang-Jun ^{[1
,2
]}

Shi, Lei ^{[1
,2
]}

Zhou, Ding-Xuan ^{[3
]}

机构：

[1] Univ Sci & Technol China, Joint Adv Res Ctr Suzhou, Suzhou 215123, Jiangshu, Peoples R China

[2] City Univ Hong Kong, Suzhou 215123, Jiangshu, Peoples R China

[3] City Univ Hong Kong, Dept Math, Kowloon, Hong Kong, Peoples R China

来源：

CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES | 2011年 / 54卷 / 03期

关键词：

multivariate approximation; Sobolev spaces; non-uniform randomized sampling; high order Parzen windows; convergence rates; RECONSTRUCTION;

D O I：

10.4153/CMB-2011-029-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider approximation of multivariate functions in Sobolev spaces by high order Parzen windows in a non-uniform sampling setting. Sampling points are neither i.i.d. nor regular, but are noised from regular grids by non-uniform shifts of a probability density function. Sample function values at sampling points are drawn according to probability measures with expected values being values of the approximated function. The approximation orders are estimated by means of regularity of the approximated function, the density function, and the order of the Parzen windows, under suitable choices of the scaling parameter.

引用

页码：566 / 576

页数：11

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