Localized/Shrinkage Kriging Predictors

Abstract

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 exhibits a shrinkage effect and is termed a localized/shrinkage kriging predictor. The predictor is compared to traditional localized kriging predictors in a case study on observations of annual accumulated precipitation. A cross-validation criterion is used in the comparison. The shrinkage predictor appears as clearly preferable to the traditional kriging predictors. A simulation study on prediction in non-stationary Gaussian random fields is conducted. The results from this study confirm that the shrinkage predictor is preferable to the traditional one. Moreover, the cross-validation criterion is found to be suitable for selection of the local neighborhood in the predictor. Lastly, the computational demands of localized predictors are very modest, hence these localized/shrinkage predictors are suitable for large scale spatial prediction problems.