To Örebro University

In various areas of modern statistical applications such as in Environmetrics, Image Processing, Epidemiology, Biology, Astronomy, Industrial Mathematics, and many others, we encounter challenges of analyzing massive data sets which are spatially observable, often presented as maps, and temporally correlated. The analysis of such data is usually performed with the goal to obtain both the spatial interpolation and the temporal prediction. In both cases, the data-generating process has to be fitted by an appropriate stochastic model which should have two main properties: (i) it should provide a good fit to the true underlying model; (ii) its structure could not be too complicated avoiding considerable estimation error appeared by fitting the model to real data. Consequently, achieving the reasonable trade-off between the model uncertainty and the parameter uncertainty is one of the most difficult questions of modern statistical theory.

We deal with this problem in the case of general spatio-temporal models by applying the LOESS predictor for both the spatial interpolation and the temporal prediction. The number of closest neighboring regions to be used in its construction is determined by cross-validation. We also discuss the computational aspects in the case of large-dimensional data and apply the theoretical findings to real data consisting of the number of influenza cases observed in the south of Germany.