Non-uniform randomized sampling for multivariate approximation by high order Parzen windows
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review
Author(s)
Related Research Unit(s)
Detail(s)
Original language | English |
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Pages (from-to) | 566-576 |
Journal / Publication | Canadian Mathematical Bulletin |
Volume | 54 |
Issue number | 3 |
Publication status | Published - Sept 2011 |
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Abstract
We consider approximation ofmultivariate 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 bymeans of regularity of the approximated function, the density function, and the order of the Parzen windows, under suitable choices of the scaling parameter. ©Canadian Mathematical Society 2011.
Research Area(s)
- Convergence rates, High order Parzen windows, Multivariate approximation, Non-uniform randomized sampling, Sobolev spaces
Citation Format(s)
Non-uniform randomized sampling for multivariate approximation by high order Parzen windows. / Zhou, Xiang-Jun; Shi, Lei; Zhou, Ding-Xuan.
In: Canadian Mathematical Bulletin, Vol. 54, No. 3, 09.2011, p. 566-576.
In: Canadian Mathematical Bulletin, Vol. 54, No. 3, 09.2011, p. 566-576.
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review