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High order Parzen windows and randomized sampling.

Authors :
Zhou, Xiang-Jun
Zhou, Ding-Xuan
Source :
Advances in Computational Mathematics; Nov2009, Vol. 31 Issue 4, p349-368, 20p
Publication Year :
2009

Abstract

In this paper high order Parzen windows stated by means of basic window functions are studied for understanding some algorithms in learning theory and randomized sampling in multivariate approximation. Learning rates are derived for the least-square regression and density estimation on bounded domains under some decay conditions on the marginal distributions near the boundary. These rates can be almost optimal when the marginal distributions decay fast and the order of the Parzen windows is large enough. For randomized sampling in shift-invariant spaces, we consider the situation when the sampling points are neither i.i.d. nor regular, but are noised from regular grids by probability density functions. The approximation orders are estimated by means of the regularity of the approximated function and the density function and the order of the Parzen windows. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
10197168
Volume :
31
Issue :
4
Database :
Complementary Index
Journal :
Advances in Computational Mathematics
Publication Type :
Academic Journal
Accession number :
44917715
Full Text :
https://doi.org/10.1007/s10444-008-9073-8