Parameter estimation for and smoothing or interpolation of spatially or spatio-temporally correlated random processes is used in many areas and often requires the solution of a large linear system based on the covariance matrix of the observations. In recent years the dataset sizes have steadily increased such that straightforward statistical tools are computationally too expensive to be used. In the univariate context, tapering, i.e., creating sparse approximate linear systems, has been shown to be an efficient tool in both the estimation and prediction setting.
In this talk we present a short review of tapering in the context of temporal and spatial statistics. Key concepts in the framework of estimation and prediction for univariate spatial processes are discussed. A pragmatic asymptotic setting for the extension of tapering to multivariate spatial processes is given and illustrated. We conclude with open problems and challenges of tapering in the context of spatio-temporal modeling.
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