The Loss of Efficiency in Kriging Prediction Caused by Misspecifications of the Covariance Structure

Abstract

A major obstacle to making sound statistical inferences based on kriging is accounting for the effect of using estimated covariance structures on the ensuing kriging predictions. One way to investigate this problem is to study the effect of using a fixed but incorrect covariance structure to produce kriging predictions. This paper gives simple and explicit bounds for the increase in the variance of prediction errors caused by misspecifying the covariance structure in certain ways. In particular, the effects of using an isotropic model when in fact a geometric anisotropy is needed are investigated. These results give insights into how well certain features of the covariance function need to be estimated in order to obtain kriging predictions that are nearly optimal.