Multivariate Integration and Approximation for Random Fields Satisfying Sacks-Ylvisaker Conditions

Open Access

1 May 1995

journal article
Published by Institute of Mathematical Statistics in The Annals of Applied Probability

Vol. 5 (2) , 518-540
https://doi.org/10.1214/aoap/1177004776

Abstract

We present sharp bounds on the minimal errors of linear estimators for multivariate integration and $L_2$-approximation. This is done for a random field whose covariance kernel is a tensor product of one-dimensional kernels that satisfy the Sacks-Ylvisaker regularity conditions.

Keywords

TENSOR
KERNEL
SHARP
L_2
MINIMAL
COVARIANCE
RANDOM FIELDS
SATISFYING SACKS YLVISAKER

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