Covariance Tapering for Prediction of Large Spatial Data Sets in Transformed Random Fields

The best linear unbiased predictor (BLUP) is called a kriging predictor and has been widely used to interpolate a spatially correlated random process in scientific areas such as geostatistics. The BLUP is identical with the conditional expectation if an underlying random field is Gaussian and consequently is the optimal predictor in the mean squared error (MSE) sense. However, if an original data takes a nonnegative value or has a skewed distribution, we frequently apply a nonlinear transformation to it to get a data which is nearer Gaussian. Then the optimality of the BLUP for the original data is unclear because it is not Gaussian. Moreover, in many cases, data sets in spatial problems are often so large that a kriging predictor is impractically time-consuming. To reduce the computational complexity, covariance tapering has been developed by Furrer et al. (2006) for large spatial data sets. In this paper we consider covariance tapering in a class of transformed Gaussian models for random elds and show that the BLUP using covariance tapering, the BLUP and the optimal predictor are asymptotically equivalent in the MSE sense if the underlying Gaussian random eld has the Matérn covariance function. This is an extension of Furrer et al. (2006). Monte Carlo simulations support theoretical results.