On estimation and prediction of geostatistical regression models via a corrected Stein's unbiased risk estimator

Abstract

We consider geostatistical regression models to predict spatial variables of interest, where likelihood‐based methods are used to estimate model parameters. It is known that parameters in the Matérn covariogram cannot be estimated well, even when increasing amounts of data are collected densely in a fixed domain. Although a best linear unbiased predictor has been proposed when model parameters are known, a predictor with estimated parameters is nonlinear and may be not the best in practice. Therefore, we propose an adjusted procedure for the likelihood‐based estimates to improve the predicted ability of the nonlinear spatial predictor. The adjusted parameter estimators based on minimizing a corrected Stein's unbiased risk estimator tend to have less bias than the conventional likelihood‐based estimators, and the resulting spatial predictor is more accurate and more stable. Statistical inference for the proposed method is justified both theoretically and numerically. To verify the practicability of the proposed method, a groundwater data set in Bangladesh is analyzed.