A sandwich smoother for spatio-temporal functional data

Abstract

Statistical analysis of spatio-temporal data has been evolving to handle increasingly large data sets. For example, the North American CORDEX program is producing daily values of climate-related variables on spatial grids with approximately 100,000 locations over 150 years. Smoothing of such massive and noisy data is essential to understanding their spatio-temporal features. It also reduces the size of the data by representing them in terms of suitable basis functions, which facilitates further computations and statistical analysis. Traditional tensor-based methods break down under the size of such massive data. We develop a penalized spline method for representing such data using a generalization of the sandwich smoother proposed by Xiao et al. (2013). Unlike the original method, our generalization treats the spatial and temporal dimensions distinctly and allows the methodology to be directly applied to non-gridded data. We demonstrate the practicality of the methodology using both simulated and real data. The new smoother, as well as the original sandwich smoother, is implemented in the hero R package.