Title: On Prediction Properties of Kriging: Uniform Error Bounds and Robustness,
Abstract: Kriging based on Gaussian random fields is widely used in reconstructing
unknown functions. The kriging method has pointwise predictive distributions
which are computationally simple. However, in many applications one would like
to predict for a range of untried points simultaneously. In this work we obtain
some error bounds for the (simple) kriging predictor under the uniform metric.
It works for a scattered set of input points in an arbitrary dimension, and
also covers the case where the covariance function of the Gaussian process is
misspecified. These results lead to a better understanding of the rate of
convergence of kriging under the Gaussian or the Matérn correlation
functions, the relationship between space-filling designs and kriging models,
and the robustness of the Matérn correlation functions.