Kriging Prediction Intervals Based on Semiparametric Bootstrap

Kriging is a widely used method for prediction, which, given observations of a (spatial) process, yields the best linear unbiased predictor of the process at a new location. The construction of corresponding prediction intervals typically relies on Gaussian assumptions. Here we show that the distribution of kriging predictors for non-Gaussian processes may be far from Gaussian, even asymptotically. This emphasizes the need for other ways to construct prediction intervals. We propose a semiparametric bootstrap method with focus on the ordinary kriging predictor. No distributional assumptions about the data generating process are needed. A simulation study for Gaussian as well as lognormal processes shows that the semiparametric bootstrap method works well. For the lognormal process we see significant improvement in coverage probability compared to traditional methods relying on Gaussian assumptions.