The correct Kriging variance estimated by bootstrapping

The classic Kriging variance formula is widely used in geostatistics and in the design and analysis of computer experiments. This paper proves that this formula is wrong. Furthermore, it shows that the formula underestimates the Kriging variance in expectation. The paper develops parametric bootstrapping to estimate the Kriging variance. The new method is tested on several artificial examples and a real-life case study. These results demonstrate that the classic formula underestimates the true Kriging variance.