Pointwise consistency of the kriging predictor with known mean and covariance functions

TL;DR

This paper investigates the conditions under which the kriging predictor with known mean and covariance functions is pointwise consistent, correcting a previous erroneous claim and using reproducing kernel Hilbert space theory.

Contribution

It clarifies the conditions for pointwise consistency of kriging predictors with known parameters, correcting prior misconceptions in the literature.

Findings

Identifies conditions for pointwise consistency of kriging

Refutes a previous claim about universal consistency

Uses reproducing kernel Hilbert space analysis

Abstract

This paper deals with several issues related to the pointwise consistency of the kriging predictor when the mean and the covariance functions are known. These questions are of general importance in the context of computer experiments. The analysis is based on the properties of approximations in reproducing kernel Hilbert spaces. We fix an erroneous claim of Yakowitz and Szidarovszky (J. Multivariate Analysis, 1985) that the kriging predictor is pointwise consistent for all continuous sample paths under some assumptions.