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1. CMB 2011 (vol 54 pp. 566)
| Non-uniform Randomized Sampling for Multivariate Approximation by High Order Parzen Windows 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.
Keywords:multivariate approximation, Sobolev spaces, non-uniform randomized sampling, high order Parzen windows, convergence rates Categories:68T05, 62J02 |

