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Estimating Space and Space-Time Covariance Functions for Large Data Sets: A Weighted Composite Likelihood Approach


  • Moreno Bevilacqua
  • Carlo Gaetan
  • Jorge Mateu
  • Emilio Porcu


In this article, we propose two methods for estimating space and space-time covariance functions from a Gaussian random field, based on the composite likelihood idea. The first method relies on the maximization of a weighted version of the composite likelihood function, while the second one is based on the solution of a weighted composite score equation. This last scheme is quite general and could be applied to any kind of composite likelihood. An information criterion for model selection based on the first estimation method is also introduced. The methods are useful for practitioners looking for a good balance between computational complexity and statistical efficiency. The effectiveness of the methods is illustrated through examples, simulation experiments, and by analyzing a dataset on ozone measurements.

Suggested Citation

  • Moreno Bevilacqua & Carlo Gaetan & Jorge Mateu & Emilio Porcu, 2012. "Estimating Space and Space-Time Covariance Functions for Large Data Sets: A Weighted Composite Likelihood Approach," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(497), pages 268-280, March.
  • Handle: RePEc:taf:jnlasa:v:107:y:2012:i:497:p:268-280
    DOI: 10.1080/01621459.2011.646928

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    Cited by:

    1. S. De Iaco & M. Palma & D. Posa, 2013. "Prediction of particle pollution through spatio-temporal multivariate geostatistical analysis: spatial special issue," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 97(2), pages 133-150, April.
    2. M. Bevilacqua & A. Fassò & C. Gaetan & E. Porcu & D. Velandia, 2016. "Covariance tapering for multivariate Gaussian random fields estimation," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 25(1), pages 21-37, March.
    3. repec:spr:testjl:v:27:y:2018:i:1:d:10.1007_s11749-017-0541-7 is not listed on IDEAS
    4. Kenne Pagui, E.C. & Salvan, A. & Sartori, N., 2015. "On full efficiency of the maximum composite likelihood estimator," Statistics & Probability Letters, Elsevier, vol. 97(C), pages 120-124.
    5. Tata Subba Rao & Sourav Das & Georgi N. Boshnakov, 2014. "A Frequency Domain Approach For The Estimation Of Parameters Of Spatio-Temporal Stationary Random Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(4), pages 357-377, July.
    6. 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.
    7. repec:bla:jtsera:v:38:y:2017:i:6:p:936-959 is not listed on IDEAS
    8. repec:esx:essedp:767 is not listed on IDEAS
    9. Moreno Bevilacqua & Alfredo Alegria & Daira Velandia & Emilio Porcu, 2016. "Composite Likelihood Inference for Multivariate Gaussian Random Fields," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 21(3), pages 448-469, September.
    10. Yun Bai & Jian Kang & Peter X.-K. Song, 2014. "Efficient pairwise composite likelihood estimation for spatial-clustered data," Biometrics, The International Biometric Society, vol. 70(3), pages 661-670, September.
    11. repec:eee:stapro:v:130:y:2017:i:c:p:115-119 is not listed on IDEAS

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