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Multivariate and multiradial Schoenberg measures with their dimension walks

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  • Alonso-Malaver, C.E.
  • Porcu, E.
  • Giraldo, R.

Abstract

The paper fixes some important properties of matrix-valued correlation functions associated to Multivariate Gaussian fields in a Euclidean space Rd. In particular, we focus (a) on the isotropic (radially symmetric) case and (b) on anisotropy obtained through isotropy between components of the lag vector. This second case includes, as special case, space–time and fully symmetric correlation functions.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:133:y:2015:i:c:p:251-265
    DOI: 10.1016/j.jmva.2014.09.001
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    References listed on IDEAS

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    1. 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.
    2. Gneiting, Tilmann, 2002. "Compactly Supported Correlation Functions," Journal of Multivariate Analysis, Elsevier, vol. 83(2), pages 493-508, November.
    3. Porcu, Emilio & Zastavnyi, Viktor, 2011. "Characterization theorems for some classes of covariance functions associated to vector valued random fields," Journal of Multivariate Analysis, Elsevier, vol. 102(9), pages 1293-1301, October.
    4. Gneiting, Tilmann, 1999. "Radial Positive Definite Functions Generated by Euclid's Hat," Journal of Multivariate Analysis, Elsevier, vol. 69(1), pages 88-119, April.
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    Cited by:

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    2. 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.

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