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Compactly Supported Correlation Functions

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  • Gneiting, Tilmann

Abstract

This article proposes compactly supported correlation functions, which parameterize the smoothness of the associated stationary and isotropic random field. The constructions are straightforward, and compact support is relevant for various ends: computationally efficient spatial prediction, fast and exact simulation, and appeal among practicioners.

Suggested Citation

  • Gneiting, Tilmann, 2002. "Compactly Supported Correlation Functions," Journal of Multivariate Analysis, Elsevier, vol. 83(2), pages 493-508, November.
    • Handle: RePEc:eee:jmvana:v:83:y:2002:i:2:p:493-508
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    References listed on IDEAS

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    1. S. Davies & P. Hall, 1999. "Fractal analysis of surface roughness by using spatial data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 3-37.
    2. Gneiting, Tilmann, 1999. "Radial Positive Definite Functions Generated by Euclid's Hat," Journal of Multivariate Analysis, Elsevier, vol. 69(1), pages 88-119, April.
    3. Kanter, Marek, 1997. "Unimodal spectral windows," Statistics & Probability Letters, Elsevier, vol. 34(4), pages 403-411, June.
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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. 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.
    3. Chiranjit Mukherjee & Prasad Kasibhatla & Mike West, 2014. "Spatially varying SAR models and Bayesian inference for high-resolution lattice data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(3), pages 473-494, June.
    4. Timothy G. Conley & Sílvia Gonçalves & Min Seong Kim & Benoit Perron, 2023. "Bootstrap inference under cross‐sectional dependence," Quantitative Economics, Econometric Society, vol. 14(2), pages 511-569, May.
    5. 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).
    6. 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.
    7. Bolin, David & Lindgren, Finn, 2013. "A comparison between Markov approximations and other methods for large spatial data sets," Computational Statistics & Data Analysis, Elsevier, vol. 61(C), pages 7-21.
    8. Kelejian, Harry H. & Prucha, Ingmar R., 2007. "HAC estimation in a spatial framework," Journal of Econometrics, Elsevier, vol. 140(1), pages 131-154, September.
    9. Jonathan Rougier & Aoibheann Brady & Jonathan Bamber & Stephen Chuter & Sam Royston & Bramha Dutt Vishwakarma & Richard Westaway & Yann Ziegler, 2023. "The scope of the Kalman filter for spatio‐temporal applications in environmental science," Environmetrics, John Wiley & Sons, Ltd., vol. 34(1), February.
    10. M. Ruiz-Medina & J. Angulo & G. Christakos & R. Fernández-Pascual, 2016. "New compactly supported spatiotemporal covariance functions from SPDEs," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 25(1), pages 125-141, March.
    11. 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.
    12. Montero, José-María, 2018. "Geostatistics: Unde venis et quo vadis? /Geoestadística:¿De dónde vienes y a dónde vas?," Estudios de Economia Aplicada, Estudios de Economia Aplicada, vol. 36, pages 81-106, Enero.
    13. 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.
    14. Moreva, Olga & Schlather, Martin, 2023. "Bivariate covariance functions of Pólya type," Journal of Multivariate Analysis, Elsevier, vol. 194(C).
    15. Dawei Zhan & Huanlai Xing, 2020. "Expected improvement for expensive optimization: a review," Journal of Global Optimization, Springer, vol. 78(3), pages 507-544, November.
    16. Guella, Jean Carlo & Menegatto, Valdir Antonio & Porcu, Emilio, 2018. "Strictly positive definite multivariate covariance functions on spheres," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 150-159.
    17. Furrer, Reinhard & Bengtsson, Thomas, 2007. "Estimation of high-dimensional prior and posterior covariance matrices in Kalman filter variants," Journal of Multivariate Analysis, Elsevier, vol. 98(2), pages 227-255, February.
    18. Jialuo Liu & Tingjin Chu & Jun Zhu & Haonan Wang, 2022. "Large spatial data modeling and analysis: A Krylov subspace approach," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(3), pages 1115-1143, September.
    19. Barry, Ronald Paul, 2005. "The local approximation of variograms in by covariance functions," Statistics & Probability Letters, Elsevier, vol. 74(2), pages 171-177, September.

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