IDEAS home Printed from https://ideas.repec.org/a/bpj/ecqcon/v30y2015i1p49-58n5.html
   My bibliography  Save this article

Numerical Methods of Karhunen–Loève Expansion for Spatial Data

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/eqc-2015-6005
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.1515/eqc-2015-6005?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bledar A. Konomi & Emily L. Kang & Ayat Almomani & Jonathan Hobbs, 2023. "Bayesian Latent Variable Co-kriging Model in Remote Sensing for Quality Flagged Observations," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 28(3), pages 423-441, September.
    2. Paciorek, Christopher J. & Lipshitz, Benjamin & Zhuo, Wei & Prabhat, . & Kaufman, Cari G. G. & Thomas, Rollin C., 2015. "Parallelizing Gaussian Process Calculations in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 63(i10).
    3. Marchetti, Yuliya & Nguyen, Hai & Braverman, Amy & Cressie, Noel, 2018. "Spatial data compression via adaptive dispersion clustering," Computational Statistics & Data Analysis, Elsevier, vol. 117(C), pages 138-153.
    4. Litvinenko, Alexander & Sun, Ying & Genton, Marc G. & Keyes, David E., 2019. "Likelihood approximation with hierarchical matrices for large spatial datasets," Computational Statistics & Data Analysis, Elsevier, vol. 137(C), pages 115-132.
    5. Peter A. Gao & Hannah M. Director & Cecilia M. Bitz & Adrian E. Raftery, 2022. "Probabilistic Forecasts of Arctic Sea Ice Thickness," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(2), pages 280-302, June.
    6. Huang Huang & Sameh Abdulah & Ying Sun & Hatem Ltaief & David E. Keyes & Marc G. Genton, 2021. "Competition on Spatial Statistics for Large Datasets," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 26(4), pages 580-595, December.
    7. Waley W. J. Liang & Herbert K. H. Lee, 2019. "Bayesian nonstationary Gaussian process models via treed process convolutions," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 13(3), pages 797-818, September.
    8. Si Cheng & Bledar A. Konomi & Georgios Karagiannis & Emily L. Kang, 2024. "Recursive nearest neighbor co‐kriging models for big multi‐fidelity spatial data sets," Environmetrics, John Wiley & Sons, Ltd., vol. 35(4), June.
    9. Jingjing Yang & Dennis D. Cox & Jong Soo Lee & Peng Ren & Taeryon Choi, 2017. "Efficient Bayesian hierarchical functional data analysis with basis function approximations using Gaussian–Wishart processes," Biometrics, The International Biometric Society, vol. 73(4), pages 1082-1091, December.
    10. Matthias Katzfuss & Joseph Guinness & Wenlong Gong & Daniel Zilber, 2020. "Vecchia Approximations of Gaussian-Process Predictions," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 25(3), pages 383-414, September.
    11. Chen, Yewen & Chang, Xiaohui & Luo, Fangzhi & Huang, Hui, 2023. "Additive dynamic models for correcting numerical model outputs," Computational Statistics & Data Analysis, Elsevier, vol. 187(C).
    12. Zilber, Daniel & Katzfuss, Matthias, 2021. "Vecchia–Laplace approximations of generalized Gaussian processes for big non-Gaussian spatial data," Computational Statistics & Data Analysis, Elsevier, vol. 153(C).
    13. Ranadeep Daw & Christopher K. Wikle, 2023. "REDS: Random ensemble deep spatial prediction," Environmetrics, John Wiley & Sons, Ltd., vol. 34(1), February.
    14. K. Shuvo Bakar, 2020. "Interpolation of daily rainfall data using censored Bayesian spatially varying model," Computational Statistics, Springer, vol. 35(1), pages 135-152, March.
    15. Caamaño-Carrillo, Christian & Bevilacqua, Moreno & López, Cristian & Morales-Oñate, Víctor, 2024. "Nearest neighbors weighted composite likelihood based on pairs for (non-)Gaussian massive spatial data with an application to Tukey-hh random fields estimation," Computational Statistics & Data Analysis, Elsevier, vol. 191(C).
    16. Isabelle Grenier & Bruno Sansó & Jessica L. Matthews, 2024. "Multivariate nearest‐neighbors Gaussian processes with random covariance matrices," Environmetrics, John Wiley & Sons, Ltd., vol. 35(3), May.
    17. Patrick Vetter & Wolfgang Schmid & Reimund Schwarze, 2013. "Efficient Approximation of the Spatial Covariance Function for Large Datasets - Analysis of Atmospheric CO2 Concentrations," Discussion Paper Series RECAP15 009, RECAP15, European University Viadrina, Frankfurt (Oder).
    18. Hossein Boojari & Majid Khaledi & Firoozeh Rivaz, 2016. "A non-homogeneous skew-Gaussian Bayesian spatial model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 25(1), pages 55-73, March.
    19. Guhaniyogi, Rajarshi & Banerjee, Sudipto, 2019. "Multivariate spatial meta kriging," Statistics & Probability Letters, Elsevier, vol. 144(C), pages 3-8.
    20. Morales-Oñate, Víctor & Crudu, Federico & Bevilacqua, Moreno, 2021. "Blockwise Euclidean likelihood for spatio-temporal covariance models," Econometrics and Statistics, Elsevier, vol. 20(C), pages 176-201.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bpj:ecqcon:v:30:y:2015:i:1:p:49-58:n:5. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Peter Golla (email available below). General contact details of provider: https://www.degruyterbrill.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.