Kriging by local polynomials

Abstract

A flexible framework for prediction of a random process with unknown trend and correlated residuals is presented. Our approach is motivated by a local parametric model, and we derive a locally optimal predictor of the process at unobserved locations. Comparisons with local regression estimation and Kriging are made, and we show that the proposed class of methods provides a bridge between these two approaches. A procedure for parameter estimation and model selection is suggested. The method is illustrated through a simulation study and through an application to European sulphate data.