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Matrix-valued isotropic covariance functions with local extrema

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  • Alegría, Alfredo
  • Emery, Xavier

Abstract

Multivariate random fields are commonly used in spatial statistics and natural science to model coregionalized variables. In this context, the matrix-valued covariance function plays a central role in capturing their spatial continuity and interdependence. This study aims to contribute to the literature on covariance modeling by proposing new parametric families of isotropic matrix-valued functions exhibiting non-monotonic behaviors, namely hole effects and cross-dimples. The benefit of the proposed models is shown on a bivariate data set consisting of concentrations of airborne particulate matter.

Suggested Citation

  • Alegría, Alfredo & Emery, Xavier, 2024. "Matrix-valued isotropic covariance functions with local extrema," Journal of Multivariate Analysis, Elsevier, vol. 200(C).
  • Handle: RePEc:eee:jmvana:v:200:y:2024:i:c:s0047259x23000969
    DOI: 10.1016/j.jmva.2023.105250
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    References listed on IDEAS

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    1. Nieto-Reyes, Alicia & Cuesta-Albertos, Juan Antonio & Gamboa, Fabrice, 2014. "A random-projection based test of Gaussianity for stationary processes," Computational Statistics & Data Analysis, Elsevier, vol. 75(C), pages 124-141.
    2. Li, Bo & Zhang, Hao, 2011. "An approach to modeling asymmetric multivariate spatial covariance structures," Journal of Multivariate Analysis, Elsevier, vol. 102(10), pages 1445-1453, November.
    3. Bellier, Edwige & Monestiez, Pascal, 2010. "A spatial covariance model with a single wave effect and a finite range," Statistics & Probability Letters, Elsevier, vol. 80(17-18), pages 1343-1347, September.
    4. 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.
    5. Lobato, Ignacio N. & Velasco, Carlos, 2004. "A Simple Test Of Normality For Time Series," Econometric Theory, Cambridge University Press, vol. 20(4), pages 671-689, August.
    6. Tatiyana V. Apanasovich & Marc G. Genton & Ying Sun, 2012. "A Valid Matérn Class of Cross-Covariance Functions for Multivariate Random Fields With Any Number of Components," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(497), pages 180-193, March.
    7. Tatiyana V. Apanasovich & Marc G. Genton, 2010. "Cross-covariance functions for multivariate random fields based on latent dimensions," Biometrika, Biometrika Trust, vol. 97(1), pages 15-30.
    8. Moreva, Olga & Schlather, Martin, 2023. "Bivariate covariance functions of Pólya type," Journal of Multivariate Analysis, Elsevier, vol. 194(C).
    9. Faouzi, Tarik & Porcu, Emilio & Bevilacqua, Moreno & Kondrashuk, Igor, 2020. "Zastavnyi operators and positive definite radial functions," Statistics & Probability Letters, Elsevier, vol. 157(C).
    10. Renxiang Wang & Juan Du & Chunsheng Ma, 2014. "Covariance Matrix Functions of Isotropic Vector Random Fields," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(10-12), pages 2081-2093, May.
    11. Noel Cressie & Andrew Zammit-Mangion, 2016. "Multivariate spatial covariance models: a conditional approach," Biometrika, Biometrika Trust, vol. 103(4), pages 915-935.
    12. Francisco Gerardo Benavides-Bravo & Roberto Soto-Villalobos & José Roberto Cantú-González & Mario A. Aguirre-López & Ángela Gabriela Benavides-Ríos, 2021. "A Quadratic–Exponential Model of Variogram Based on Knowing the Maximal Variability: Application to a Rainfall Time Series," Mathematics, MDPI, vol. 9(19), pages 1-20, October.
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