IDEAS home Printed from https://ideas.repec.org/a/bla/istatr/v89y2021i1p36-53.html
   My bibliography  Save this article

On Some Characteristics of Gaussian Covariance Functions

Author

Listed:
  • Sandra De Iaco
  • Donato Posa
  • Claudia Cappello
  • Sabrina Maggio

Abstract

The concepts of isotropy/anisotropy and separability/non‐separability of a covariance function are strictly related. If a covariance function is separable, it cannot be isotropic or geometrically anisotropic, except for the Gaussian covariance function, which is the only model both separable and isotropic. In this paper, some interesting results concerning the Gaussian covariance model and its properties related to isotropy and separability are given, and moreover, some examples are provided. Finally, a discussion on asymmetric models, with Gaussian marginals, is furnished and the strictly positive definiteness condition is discussed.

Suggested Citation

  • Sandra De Iaco & Donato Posa & Claudia Cappello & Sabrina Maggio, 2021. "On Some Characteristics of Gaussian Covariance Functions," International Statistical Review, International Statistical Institute, vol. 89(1), pages 36-53, April.
    • Handle: RePEc:bla:istatr:v:89:y:2021:i:1:p:36-53
    DOI: 10.1111/insr.12403
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/insr.12403
    Download Restriction: no
    File URL: https://libkey.io/10.1111/insr.12403?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
    ---><---

    References listed on IDEAS

    as
    1. Peter Guttorp & Tilmann Gneiting, 2006. "Studies in the history of probability and statistics XLIX On the Matern correlation family," Biometrika, Biometrika Trust, vol. 93(4), pages 989-995, December.
    2. Wang, Bo & Xu, Aiping, 2019. "Gaussian process methods for nonparametric functional regression with mixed predictors," Computational Statistics & Data Analysis, Elsevier, vol. 131(C), pages 80-90.
    3. Michael L. Stein, 2005. "Space-Time Covariance Functions," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 310-321, March.
    4. 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.
    5. He, Heping & Severini, Thomas A., 2016. "A flexible approach to inference in semiparametric regression models with correlated errors using Gaussian processes," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 316-329.
    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. 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).
    2. 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.
    3. Harrison Quick & Sudipto Banerjee & Bradley P. Carlin, 2015. "Bayesian modeling and analysis for gradients in spatiotemporal processes," Biometrics, The International Biometric Society, vol. 71(3), pages 575-584, September.
    4. Girard, Didier A., 2016. "Asymptotic near-efficiency of the “Gibbs-energy and empirical-variance” estimating functions for fitting Matérn models — I: Densely sampled processes," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 191-197.
    5. 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.
    6. Frank Davenport, 2017. "Estimating standard errors in spatial panel models with time varying spatial correlation," Papers in Regional Science, Wiley Blackwell, vol. 96, pages 155-177, March.
    7. Daniel Griffith, 2010. "Modeling spatio-temporal relationships: retrospect and prospect," Journal of Geographical Systems, Springer, vol. 12(2), pages 111-123, June.
    8. 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.
    9. Hansen, Linda V. & Thorarinsdottir, Thordis L., 2013. "A note on moving average models for Gaussian random fields," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 850-855.
    10. Heinrich, Claudio & Pakkanen, Mikko S. & Veraart, Almut E.D., 2019. "Hybrid simulation scheme for volatility modulated moving average fields," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 166(C), pages 224-244.
    11. Marcus L. Nascimento & Kelly C. M. Gonçalves & Mario Jorge Mendonça, 2023. "Spatio-Temporal Instrumental Variables Regression with Missing Data: A Bayesian Approach," Computational Economics, Springer;Society for Computational Economics, vol. 62(1), pages 29-47, June.
    12. Kelly R. Moran & Matthew W. Wheeler, 2022. "Fast increased fidelity samplers for approximate Bayesian Gaussian process regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(4), pages 1198-1228, September.
    13. 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.
    14. 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.
    15. Christopher Wikle & Mevin Hooten, 2010. "A general science-based framework for dynamical spatio-temporal models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(3), pages 417-451, November.
    16. Richardson, Robert & Kottas, Athanasios & Sansó, Bruno, 2017. "Flexible integro-difference equation modeling for spatio-temporal data," Computational Statistics & Data Analysis, Elsevier, vol. 109(C), pages 182-198.
    17. 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.
    18. Nesbitt, Peter & Blake, Lewis R. & Lamas, Patricio & Goycoolea, Marcos & Pagnoncelli, Bernardo K. & Newman, Alexandra & Brickey, Andrea, 2021. "Underground mine scheduling under uncertainty," European Journal of Operational Research, Elsevier, vol. 294(1), pages 340-352.
    19. Unn Dahlén & Johan Lindström & Marko Scholze, 2020. "Spatiotemporal reconstructions of global CO2‐fluxes using Gaussian Markov random fields," Environmetrics, John Wiley & Sons, Ltd., vol. 31(4), June.
    20. McDonald, C.P. & Bennington, V. & Urban, N.R. & McKinley, G.A., 2012. "1-D test-bed calibration of a 3-D Lake Superior biogeochemical model," Ecological Modelling, Elsevier, vol. 225(C), pages 115-126.

    More about this item

    Statistics

    Access and download statistics

    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:bla:istatr:v:89:y:2021:i:1:p:36-53. 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: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/isiiinl.html .

    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.