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Large spatial datasets are becoming ubiquitous in environmental sciences withthe explosion in the amount of data produced by sensors that monitor andmeasure the Earth system. Consequently, the geostatistical analysis of thesedata requires adequate methods. Richer datasets lead to more complex modelingbut may also prevent from using classical techniques. Indeed, the krigingpredictor is not straightforwarldly available as it requires the inversion ofthe covariance matrix of the data. The challenge of handling such datasets istherefore to extract the maximum of information they contain while ensuring thenumerical tractability of the associated inference and prediction algorithms.The different approaches that have been developed in the literature to addressthis problem can be classified into two families, both aiming at making theinversion of the covariance matrix computationally feasible. The covariancetapering approach circumvents the problem by enforcing the sparsity of thecovariance matrix, making it invertible in a reasonable computation time. Thesecond available approach assumes a low rank representation of the covariancefunction. While both approaches have their drawbacks, we propose a way tocombine them and benefit from their advantages. The covariance model is assumedto have the form low rank plus sparse. The choice of the basis functionssustaining the low rank component is data driven and is achieved through aselection procedure, thus alleviating the computational burden of the low rankpart. This model expresses as a spatial random effects model and the estimationof the parameters is conducted through a step by step approach treating eachscale separately. The resulting model can account for second order nonstationarity and handle large volumes of data.

Combining covariance tapering and lasso driven low rank decomposition for the kriging of large spatial datasets