Statistical Tests for Cross-Validation of Kriging Models

We derive new statistical tests for leave-one-out cross-validation of Kriging models. Graphically, we present these tests as scatterplots augmented with confi…dence intervals. We may wish to avoid extrapolation, which we de…fine
as prediction of the output for a point that is a vertex of the convex hull of the
given input combinations. Moreover, we may use bootstrapping to estimate the
true variance of the Kriging predictor. The resulting tests (with or without extrapolation or bootstrapping) have type-I and type-II error probabilities, which
we estimate through Monte Carlo experiments. To illustrate the application of
our tests, we use an example with two inputs and the popular borehole example
with eight inputs.