IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v195y2023ics0047259x23000027.html
   My bibliography  Save this article

Penalized Whittle likelihood for spatial data

Author

Listed:
  • Chen, Kun
  • Chan, Ngai Hang
  • Yau, Chun Yip
  • Hu, Jie

Abstract

Inference for spatial data is challenging because fitting an appropriate parametric model is often difficult. The penalized likelihood-type approach has been successfully developed for various nonparametric function estimation problems in time series analysis. However, it has not been well developed in spatial analysis. In this paper, a penalized Whittle likelihood approach is developed for nonparametric estimation of spectral density functions for regularly spaced spatial data. In particular, the estimated spectral density is the minimizer of a criterion which is developed based on the Whittle likelihood and a penalty for roughness. This approach aggregates several popular nonparametric density estimation methods into a coherent framework. Asymptotic properties of the proposed estimator are derived under mild assumptions without assuming Gaussianity. In addition, a computationally efficient method is developed to optimize the penalized likelihood function. Simulation results and real data examples are also provided to illustrate the finite sample performances of the methodology.

Suggested Citation

  • Chen, Kun & Chan, Ngai Hang & Yau, Chun Yip & Hu, Jie, 2023. "Penalized Whittle likelihood for spatial data," Journal of Multivariate Analysis, Elsevier, vol. 195(C).
    • Handle: RePEc:eee:jmvana:v:195:y:2023:i:c:s0047259x23000027
    DOI: 10.1016/j.jmva.2023.105156
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X23000027
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2023.105156?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. Fuentes, Montserrat, 2007. "Approximate Likelihood for Large Irregularly Spaced Spatial Data," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 321-331, March.
    2. Michael L. Stein & Zhiyi Chi & Leah J. Welty, 2004. "Approximating likelihoods for large spatial data sets," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(2), pages 275-296, May.
    3. Gupta, Abhimanyu, 2018. "Autoregressive spatial spectral estimates," Journal of Econometrics, Elsevier, vol. 203(1), pages 80-95.
    4. Wu, Wei-Ying & Lim, Chae Young & Xiao, Yimin, 2013. "Tail estimation of the spectral density for a stationary Gaussian random field," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 74-91.
    5. Yasumasa Matsuda & Yoshihiro Yajima, 2009. "Fourier analysis of irregularly spaced data on Rd," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 191-217, January.
    6. Robinson, Peter, 2008. "Developments in the analysis of spatial data," LSE Research Online Documents on Economics 25473, London School of Economics and Political Science, LSE Library.
    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. repec:cep:stiecm:/2013/568 is not listed on IDEAS
    2. Delgado, Miguel A. & Robinson, Peter M., 2015. "Non-nested testing of spatial correlation," Journal of Econometrics, Elsevier, vol. 187(1), pages 385-401.
    3. Giovanna Jona Lasinio & Gianluca Mastrantonio & Alessio Pollice, 2013. "Discussing the “big n problem”," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 22(1), pages 97-112, March.
    4. Arthur P. Guillaumin & Adam M. Sykulski & Sofia C. Olhede & Frederik J. Simons, 2022. "The Debiased Spatial Whittle likelihood," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(4), pages 1526-1557, September.
    5. Shibin Zhang, 2022. "Automatic estimation of spatial spectra via smoothing splines," Computational Statistics, Springer, vol. 37(2), pages 565-590, April.
    6. Gupta, Abhimanyu, 2018. "Autoregressive spatial spectral estimates," Journal of Econometrics, Elsevier, vol. 203(1), pages 80-95.
    7. Matthew J. Heaton & Abhirup Datta & Andrew O. Finley & Reinhard Furrer & Joseph Guinness & Rajarshi Guhaniyogi & Florian Gerber & Robert B. Gramacy & Dorit Hammerling & Matthias Katzfuss & Finn Lindgr, 2019. "A Case Study Competition Among Methods for Analyzing Large Spatial Data," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 24(3), pages 398-425, September.
    8. Eidsvik, Jo & Finley, Andrew O. & Banerjee, Sudipto & Rue, Håvard, 2012. "Approximate Bayesian inference for large spatial datasets using predictive process models," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1362-1380.
    9. Gupta, A, 2015. "Autoregressive Spatial Spectral Estimates," Economics Discussion Papers 14458, University of Essex, Department of Economics.
    10. 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.
    11. Kurisu, Daisuke, 2019. "On nonparametric inference for spatial regression models under domain expanding and infill asymptotics," Statistics & Probability Letters, Elsevier, vol. 154(C), pages 1-1.
    12. Jun, Mikyoung, 2014. "Matérn-based nonstationary cross-covariance models for global processes," Journal of Multivariate Analysis, Elsevier, vol. 128(C), pages 134-146.
    13. 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.
    14. Andrew O. Finley & Sudipto Banerjee & Patrik Waldmann & Tore Ericsson, 2009. "Hierarchical Spatial Modeling of Additive and Dominance Genetic Variance for Large Spatial Trial Datasets," Biometrics, The International Biometric Society, vol. 65(2), pages 441-451, June.
    15. Padoan, Simone A. & Bevilacqua, Moreno, 2015. "Analysis of Random Fields Using CompRandFld," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 63(i09).
    16. Håvard Rue & Sara Martino & Nicolas Chopin, 2009. "Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 319-392, April.
    17. Matthias Katzfuss, 2017. "A Multi-Resolution Approximation for Massive Spatial Datasets," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(517), pages 201-214, January.
    18. Yasumasa Matsuda & Yoshihiro Yajima, 2009. "Fourier analysis of irregularly spaced data on Rd," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 191-217, January.
    19. Schmidt, Paul & Mühlau, Mark & Schmid, Volker, 2017. "Fitting large-scale structured additive regression models using Krylov subspace methods," Computational Statistics & Data Analysis, Elsevier, vol. 105(C), pages 59-75.
    20. Yasumasa Matsuda, 2013. "Generalized Whittle Estimate For Nonstationary Spatial Data," TERG Discussion Papers 305, Graduate School of Economics and Management, Tohoku University.
    21. 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.

    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:eee:jmvana:v:195:y:2023:i:c:s0047259x23000027. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.