IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v83y2013i3p850-855.html
   My bibliography  Save this article

A note on moving average models for Gaussian random fields

Author

Listed:
  • Hansen, Linda V.
  • Thorarinsdottir, Thordis L.

Abstract

The class of moving average models offers a flexible modeling framework for Gaussian random fields with many well known models such as the Matérn covariance family and the Gaussian covariance falling under this framework. Moving average models may also be viewed as a kernel smoothing of a Lévy basis, a general modeling framework which includes several types of non-Gaussian models. We propose a new one-parameter spatial correlation model which arises from a power kernel and show that the associated Hausdorff dimension of the sample paths can take any value between 2 and 3. As a result, the model offers similar flexibility in the fractal properties of the resulting field as the Matérn model.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:3:p:850-855
    DOI: 10.1016/j.spl.2012.12.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715212004580
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2012.12.009?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. 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. Gneiting, Tilmann & Kleiber, William & Schlather, Martin, 2010. "Matérn Cross-Covariance Functions for Multivariate Random Fields," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 1167-1177.
    3. Scheuerer, Michael, 2010. "Regularity of the sample paths of a general second order random field," Stochastic Processes and their Applications, Elsevier, vol. 120(10), pages 1879-1897, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.

    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. 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.
    2. 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).
    3. Kleiber, William & Nychka, Douglas, 2012. "Nonstationary modeling for multivariate spatial processes," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 76-91.
    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. Philip Dörr & Bruno Ebner & Norbert Henze, 2021. "A new test of multivariate normality by a double estimation in a characterizing PDE," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(3), pages 401-427, April.
    7. Emilio Porcu & Moreno Bevilacqua & Marc G. Genton, 2016. "Spatio-Temporal Covariance and Cross-Covariance Functions of the Great Circle Distance on a Sphere," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 888-898, April.
    8. 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.
    9. 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.
    10. 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.
    11. Silius M. Vandeskog & Sara Martino & Daniela Castro-Camilo & Håvard Rue, 2022. "Modelling Sub-daily Precipitation Extremes with the Blended Generalised Extreme Value Distribution," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(4), pages 598-621, December.
    12. May, Paul & Biesecker, Matthew & Rekabdarkolaee, Hossein Moradi, 2022. "Response envelopes for linear coregionalization models," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    13. Laura Serra & Claudio Detotto & Marco Vannini, 2022. "Public lands as a mitigator of wildfire burned area using a spatio-temporal model applied in Sardinia," Letters in Spatial and Resource Sciences, Springer, vol. 15(3), pages 621-635, December.
    14. Akim Adekpedjou & Sophie Dabo‐Niang, 2021. "Semiparametric estimation with spatially correlated recurrent events," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(4), pages 1097-1126, December.
    15. Claudia Cappello & Sandra De Iaco & Monica Palma, 2022. "Computational advances for spatio-temporal multivariate environmental models," Computational Statistics, Springer, vol. 37(2), pages 651-670, April.
    16. Alonso-Malaver, C.E. & Porcu, E. & Giraldo, R., 2015. "Multivariate and multiradial Schoenberg measures with their dimension walks," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 251-265.
    17. Cavoretto, Roberto & De Rossi, Alessandra & Qiao, Hanli, 2018. "Topology analysis of global and local RBF transformations for image registration," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 147(C), pages 52-72.
    18. Moreva, Olga & Schlather, Martin, 2023. "Bivariate covariance functions of Pólya type," Journal of Multivariate Analysis, Elsevier, vol. 194(C).
    19. Ghada Atteia & Nagwan Abdel Samee & El-Sayed M. El-Kenawy & Abdelhameed Ibrahim, 2022. "CNN-Hyperparameter Optimization for Diabetic Maculopathy Diagnosis in Optical Coherence Tomography and Fundus Retinography," Mathematics, MDPI, vol. 10(18), pages 1-30, September.
    20. Lim, Chae Young & Wu, Wei-Ying, 2022. "Conditions on which cokriging does not do better than kriging," Journal of Multivariate Analysis, Elsevier, vol. 192(C).

    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:stapro:v:83:y:2013:i:3:p:850-855. 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.