Title: Reduced Basis Kriging for Big Spatial Fields

Author(s): Karl Pazdernik, Ranjan Maitra, Douglas Nychka and Stephan Sain
Issue: Volume 80 Series A Part 2 Year 2018
Pages: 280 -- 300
In spatial statistics, a common method for prediction over a Gaussian random field (GRF) is maximum likelihood estimation combined with kriging. For massive data sets, kriging is computationally intensive, both in terms of CPU time and memory, and so fixed rank kriging has been proposed as a solution. The method however still involves operations on large matrices, so we develop an alteration to this method by utilizing the approximations made in fixed rank kriging combined with restricted maximum likelihood estimation and sparse matrix methodology. Experiments show that our methodology can provide additional gains in computational efficiency over fixed-rank kriging without loss of accuracy in prediction. The methodology is applied to climate data archived by the United States National Climate Data Center, with very good results.
AMS (2000) subject classification. Primary 62H11; Secondary 62P12.
Keywords and phrases: Kriging, Fixed rank kriging, Gaussian random field, Sparse matrix, Spatial prediction, Maximum likelihood estimation, Bandwidth, Best linear unbiased predictor.