Comments on: Comparing and selecting spatial predictors using local criteria

Abstract

Bradley et al. (2014) select between competing spatial predictors, including traditional stationary kriging and several non-stationary and reduced rankmodels, based on expected local squared prediction error. The inclusion of reduced rankmodels as candidate predictors warrants further discussion, as the performance of these predictors has recently been questioned by Stein (2014), largely on the basis of the Kullback–Leibler divergence between the low rank approximation and the true data generating measure. Applications in Stein (2014) further show that reduced rank methods can result in inefficient spatial interpolation as measured by mean squared prediction error. In their simulation study (Bradley et al. 2014), focus on evaluating themean squared prediction errors of the Locally Selected Predictor as a number of parameters of the simulation, including the signal to noise ratio and the neighborhood used to select