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Strict positive definiteness of multivariate covariance functions on compact two-point homogeneous spaces

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  • Bonfim, Rafaela N.
  • Menegatto, Valdir A.

Abstract

The authors provide a characterization of the continuous and isotropic multivariate covariance functions associated to a Gaussian random field with index set varying over a compact two-point homogeneous space. Sufficient conditions for the strict positive definiteness based on this characterization are presented. Under the assumption that the space is not a sphere, a necessary and sufficient condition is given for the continuous and isotropic multivariate covariance function to be strictly positive definite. Under the same assumption, an alternative necessary and sufficient condition is also provided for the strict positive definiteness of a continuous and isotropic bivariate covariance function based on the main diagonal entries in the matrix representation for the covariance function.

Suggested Citation

  • Bonfim, Rafaela N. & Menegatto, Valdir A., 2016. "Strict positive definiteness of multivariate covariance functions on compact two-point homogeneous spaces," Journal of Multivariate Analysis, Elsevier, vol. 152(C), pages 237-248.
    • Handle: RePEc:eee:jmvana:v:152:y:2016:i:c:p:237-248
    DOI: 10.1016/j.jmva.2016.09.004
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. 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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