NORGES TEKNISK-NATURVITENSKAPELIGE UNIVERSITET

The objective of the study is to improve the robustness and flexibility of spatial kriging predictors with respect to deviations from spatial stationarity assumptions. A predictor based on a non-stationary Gaussian random field is defined. The model parameters are inferred in an empirical Bayesian setting, using observations in a local neighborhood and a prior model assessed from the global set of observations. The localized predictor appears with a shrinkage effect and is coined a localized/shrinkage kriging predictor. The predictor is compared to traditional localized kriging predictors in a case study on observations of annual cumulated precipitation. A crossvalidation criterion is used in the comparision. The shrinkage predictor appears as uniformly preferable to the traditional kriging predictors. A simulation study on prediction in non-stationary Gaussian random fields is conducted. The results from this study confirms that the shrinkage predictor is favorable to the traditional ones. Moreover, the crossvalidation criterion is found to be suitable for selection of predictor. Lastly, the shrinkage predictor appears as particularly robust towards spatially varying expectation functions. 1