Robustness in spatial studies I: minimax prediction

Abstract

We develop and test robust methods for estimation and for prediction in spatial studies. We assume that a stochastic process is measured, with error, at various locations. The variance/covariance structures of this process and of the measurement errors are only approximately known; in the face of these uncertainties one is to do robust estimation and prediction. We obtain a minimax linear predictor, in which mean squared error loss is first maximized over neighbourhoods quantifying the various sources of model uncertainty, and then minimized over the coefficients of the predictor subject to a constraint of unbiasedness. Robustifications of these methods are then introduced. These are based on generalized M-estimators, and are robust against contaminated error distributions. In a simulation study the procedures afford a substantial level of robustness when the model inadequacies are present, while being almost as efficient as more classical methods otherwise. Copyright © 2004 John Wiley & Sons, Ltd.