IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v150y2016icp245-266.html
   My bibliography  Save this article

On the consistency of inversion-free parameter estimation for Gaussian random fields

Author

Listed:
  • Keshavarz, Hossein
  • Scott, Clayton
  • Nguyen, XuanLong

Abstract

Gaussian random fields are a powerful tool for modeling environmental processes. For high dimensional samples, classical approaches for estimating the covariance parameters require highly challenging and massive computations, such as the evaluation of the Cholesky factorization or solving linear systems. Recently, Anitescu et al. (2014) proposed a fast and scalable algorithm which does not need such burdensome computations. The main focus of this article is to study the asymptotic behavior of the algorithm of Anitescu et al. (ACS) for regular and irregular grids in the increasing domain setting. Consistency, minimax optimality and asymptotic normality of this algorithm are proved under mild differentiability conditions on the covariance function. Despite the fact that ACS’s method entails a non-concave maximization, our results hold for any stationary point of the objective function. A numerical study is presented to evaluate the efficiency of this algorithm for large data sets.

Suggested Citation

  • Keshavarz, Hossein & Scott, Clayton & Nguyen, XuanLong, 2016. "On the consistency of inversion-free parameter estimation for Gaussian random fields," Journal of Multivariate Analysis, Elsevier, vol. 150(C), pages 245-266.
    • Handle: RePEc:eee:jmvana:v:150:y:2016:i:c:p:245-266
    DOI: 10.1016/j.jmva.2016.06.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X16300422
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2016.06.003?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. Kaufman, Cari G. & Schervish, Mark J. & Nychka, Douglas W., 2008. "Covariance Tapering for Likelihood-Based Estimation in Large Spatial Data Sets," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1545-1555.
    2. Zhang, Hao, 2004. "Inconsistent Estimation and Asymptotically Equal Interpolations in Model-Based Geostatistics," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 250-261, January.
    3. Ying, Zhiliang, 1991. "Asymptotic properties of a maximum likelihood estimator with data from a Gaussian process," Journal of Multivariate Analysis, Elsevier, vol. 36(2), pages 280-296, February.
    4. Bachoc, François, 2014. "Asymptotic analysis of the role of spatial sampling for covariance parameter estimation of Gaussian processes," Journal of Multivariate Analysis, Elsevier, vol. 125(C), pages 1-35.
    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. Bachoc, François & Lagnoux, Agnès & Nguyen, Thi Mong Ngoc, 2017. "Cross-validation estimation of covariance parameters under fixed-domain asymptotics," Journal of Multivariate Analysis, Elsevier, vol. 160(C), pages 42-67.
    2. Wenpin Tang & Lu Zhang & Sudipto Banerjee, 2021. "On identifiability and consistency of the nugget in Gaussian spatial process models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(5), pages 1044-1070, November.
    3. François Bachoc & Emile Contal & Hassan Maatouk & Didier Rullière, 2017. "Gaussian processes for computer experiments," Post-Print hal-01665936, HAL.
    4. Bachoc, François & Bevilacqua, Moreno & Velandia, Daira, 2019. "Composite likelihood estimation for a Gaussian process under fixed domain asymptotics," Journal of Multivariate Analysis, Elsevier, vol. 174(C).
    5. 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.
    6. Zhang, Tonglin, 2017. "An example of inconsistent MLE of spatial covariance parameters under increasing domain asymptotics," Statistics & Probability Letters, Elsevier, vol. 120(C), pages 108-113.
    7. Victor De Oliveira & Zifei Han, 2022. "On Information About Covariance Parameters in Gaussian Matérn Random Fields," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(4), pages 690-712, December.
    8. Hong, Yiping & Zhou, Zaiying & Yang, Ying, 2020. "Hypothesis testing for the smoothness parameter of Matérn covariance model on a regular grid," Journal of Multivariate Analysis, Elsevier, vol. 177(C).
    9. Furrer, Reinhard & Bachoc, François & Du, Juan, 2016. "Asymptotic properties of multivariate tapering for estimation and prediction," Journal of Multivariate Analysis, Elsevier, vol. 149(C), pages 177-191.
    10. Bachoc, François, 2014. "Asymptotic analysis of the role of spatial sampling for covariance parameter estimation of Gaussian processes," Journal of Multivariate Analysis, Elsevier, vol. 125(C), pages 1-35.
    11. 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.
    12. Bevilacqua, Moreno & Caamaño-Carrillo, Christian & Porcu, Emilio, 2022. "Unifying compactly supported and Matérn covariance functions in spatial statistics," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    13. 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.
    14. Bachoc, François, 2013. "Cross Validation and Maximum Likelihood estimations of hyper-parameters of Gaussian processes with model misspecification," Computational Statistics & Data Analysis, Elsevier, vol. 66(C), pages 55-69.
    15. Maitreyee Bose & James S. Hodges & Sudipto Banerjee, 2018. "Toward a diagnostic toolkit for linear models with Gaussian‐process distributed random effects," Biometrics, The International Biometric Society, vol. 74(3), pages 863-873, September.
    16. Zhou, Yuzhen & Xiao, Yimin, 2018. "Joint asymptotics for estimating the fractal indices of bivariate Gaussian processes," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 56-72.
    17. Lim, Chae Young & Chen, Chien-Hung & Wu, Wei-Ying, 2017. "Numerical instability of calculating inverse of spatial covariance matrices," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 182-188.
    18. Rajala, T. & Penttinen, A., 2014. "Bayesian analysis of a Gibbs hard-core point pattern model with varying repulsion range," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 530-541.
    19. Roman Flury & Reinhard Furrer, 2021. "Discussion on Competition for Spatial Statistics for Large Datasets," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 26(4), pages 599-603, December.
    20. 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:150:y:2016:i:c:p:245-266. 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.