Numerical Methods of Karhunen–Loève Expansion for Spatial Data

Hu Juan () and Zhang Hao ()
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Hu Juan: Department of Mathematical Sciences, DePaul University, Chicago, IL 60614, USA
Zhang Hao: Department of Statistics, Purdue University, West Lafayette, IN 40907, USA

Stochastics and Quality Control, 2015, vol. 30, issue 1, 49-58

Abstract: With the development of technology, a large amount of spatial data are usually observed in many applications. These massive spatial data impose a challenge to the traditional spatial data analysis primarily because of the large covariance matrix. One way to overcome the computation burden is to utilize a low rank model. The optimal low rank model is provided by the Karhunen–Loève (KL) expansion of the spatial process. However, the inference and prediction of the spatial data require an efficient algorithm for the KL expansion. In this paper, we compare four algorithms that have been proposed to numerically obtain the KL expansion. It is found that the Gaussian quadrature method outperforms the others for spatial processes.

Keywords: Galerkin Projection; Karhunen–Loève Expansion; Massive Spatial Data; Spatial Interpolation; Woodbury Formula (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1515/eqc-2015-6005

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