Non-uniform randomized sampling for multivariate approximation by high order Parzen windows

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

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Author(s)

  • Xiang-Jun Zhou
  • Lei Shi
  • Ding-Xuan Zhou

Related Research Unit(s)

Detail(s)

Original languageEnglish
Pages (from-to)566-576
Journal / PublicationCanadian Mathematical Bulletin
Volume54
Issue number3
Publication statusPublished - Sept 2011

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.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review