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

Author

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

Abstract

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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    Citations

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    Cited by:

    1. 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.
    2. Guillermo Ferreira & Jorge Mateu & Emilio Porcu, 2018. "Spatio-temporal analysis with short- and long-memory dependence: a state-space approach," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(1), pages 221-245, March.
    3. Moreno Bevilacqua & Christian Caamaño‐Carrillo & Carlo Gaetan, 2020. "On modeling positive continuous data with spatiotemporal dependence," Environmetrics, John Wiley & Sons, Ltd., vol. 31(7), November.
    4. 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.
    5. Moreno Bevilacqua & Christian Caamaño-Carrillo & Reinaldo B. Arellano-Valle & Camilo Gómez, 2022. "A class of random fields with two-piece marginal distributions for modeling point-referenced data with spatial outliers," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(3), pages 644-674, September.
    6. Edwards, Matthew & Castruccio, Stefano & Hammerling, Dorit, 2020. "Marginally parameterized spatio-temporal models and stepwise maximum likelihood estimation," Computational Statistics & Data Analysis, Elsevier, vol. 151(C).
    7. 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.
    8. T. Subba Rao & Gyorgy Terdik, 2017. "A New Covariance Function and Spatio-Temporal Prediction (Kriging) for A Stationary Spatio-Temporal Random Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(6), pages 936-959, November.
    9. repec:esx:essedp:767 is not listed on IDEAS
    10. Moreno Bevilacqua & Christian Caamaño‐Carrillo & Reinaldo B. Arellano‐Valle & Víctor Morales‐Oñate, 2021. "Non‐Gaussian geostatistical modeling using (skew) t processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(1), pages 212-245, March.
    11. Chung, Ray S.W. & So, Mike K.P. & Chu, Amanda M.Y. & Chan, Thomas W.C., 2020. "Regularization of Bayesian quasi-likelihoods constructed from complex estimating functions," Computational Statistics & Data Analysis, Elsevier, vol. 150(C).
    12. 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.
    13. 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.
    14. Zifeng Zhao & Peng Shi & Xiaoping Feng, 2021. "Knowledge Learning of Insurance Risks Using Dependence Models," INFORMS Journal on Computing, INFORMS, vol. 33(3), pages 1177-1196, July.
    15. Erin M. Schliep & Christopher K. Wikle & Ranadeep Daw, 2023. "Correcting for informative sampling in spatial covariance estimation and kriging predictions," Journal of Geographical Systems, Springer, vol. 25(4), pages 587-613, October.
    16. 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.
    17. 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).
    18. 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).
    19. 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.
    20. 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.
    21. Emilio Porcu & Philip A. White, 2022. "Random fields on the hypertorus: Covariance modeling and applications," Environmetrics, John Wiley & Sons, Ltd., vol. 33(1), February.
    22. 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.
    23. Ip, Ryan H.L. & Li, W.K., 2017. "A class of valid Matérn cross-covariance functions for multivariate spatio-temporal random fields," Statistics & Probability Letters, Elsevier, vol. 130(C), pages 115-119.

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