Efficient estimation for nonparametric spatio-temporal models with nonparametric autocorrelated errors

Spatio-temporally correlated data appear in many environmental studies, and consequently, there is an increasing demand for estimation methods that take account of spatio-temporal (ST) correlation and thereby improve the accuracy of estimation. In this paper, we propose an estimation procedure that improves efficiency, which is based upon a nonparametric pre-whitening transformation of the dependent variable that must be estimated from the data. The asymptotic normality of the proposed estimators is established under mild conditions. We demonstrate, using both simulation and case studies, that the proposed estimators are more efficient than the traditional locally linear methods which fail to account for ST correlation.