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Numerical Methods of Karhunen–Loève Expansion for Spatial Data

Author

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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)

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.

Suggested Citation

  • Hu Juan & Zhang Hao, 2015. "Numerical Methods of Karhunen–Loève Expansion for Spatial Data," Stochastics and Quality Control, De Gruyter, vol. 30(1), pages 49-58, June.
    • Handle: RePEc:bpj:ecqcon:v:30:y:2015:i:1:p:49-58:n:5
    DOI: 10.1515/eqc-2015-6005
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    References listed on IDEAS

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    1. Sudipto Banerjee & Alan E. Gelfand & Andrew O. Finley & Huiyan Sang, 2008. "Gaussian predictive process models for large spatial data sets," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(4), pages 825-848, September.
    2. Noel Cressie & Gardar Johannesson, 2008. "Fixed rank kriging for very large spatial data sets," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 209-226, February.
    3. Huiyan Sang & Jianhua Z. Huang, 2012. "A full scale approximation of covariance functions for large spatial data sets," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 74(1), pages 111-132, January.
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