Rights statement: This is the author’s version of a work that was accepted for publication in Spatial Statistics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Spatial Statistics, 40, 2020 DOI: 10.1016/j.spasta.2020.100448
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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
}
TY - JOUR
T1 - Families of covariance functions for bivariate random fields on spheres
AU - Bevilacqua, M.
AU - Diggle, P.J.
AU - Porcu, E.
N1 - This is the author’s version of a work that was accepted for publication in Spatial Statistics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Spatial Statistics, 40, 2020 DOI: 10.1016/j.spasta.2020.100448
PY - 2020/12/1
Y1 - 2020/12/1
N2 - This paper proposes a new class of covariance functions for bivariate random fields on spheres, having the same properties as the bivariate Matérn model proposed in Euclidean spaces. The new class depends on the geodesic distance on a sphere; it allows for indexing differentiability (in the mean square sense) and fractal dimensions of the components of any bivariate Gaussian random field having such covariance structure. We find parameter conditions ensuring positive definiteness. We discuss other possible models and illustrate our findings through a simulation study, where we explore the performance of maximum likelihood estimation method for the parameters of the new covariance function. A data illustration then follows, through a bivariate data set of temperatures and precipitations, observed over a large portion of the Earth, provided by the National Oceanic and Atmospheric Administration Earth System Research Laboratory.
AB - This paper proposes a new class of covariance functions for bivariate random fields on spheres, having the same properties as the bivariate Matérn model proposed in Euclidean spaces. The new class depends on the geodesic distance on a sphere; it allows for indexing differentiability (in the mean square sense) and fractal dimensions of the components of any bivariate Gaussian random field having such covariance structure. We find parameter conditions ensuring positive definiteness. We discuss other possible models and illustrate our findings through a simulation study, where we explore the performance of maximum likelihood estimation method for the parameters of the new covariance function. A data illustration then follows, through a bivariate data set of temperatures and precipitations, observed over a large portion of the Earth, provided by the National Oceanic and Atmospheric Administration Earth System Research Laboratory.
KW - Great-circle distance
KW - Cross correlation
KW - F class
KW - Matérn class
KW - Mean square differentiability
U2 - 10.1016/j.spasta.2020.100448
DO - 10.1016/j.spasta.2020.100448
M3 - Journal article
VL - 40
JO - Spatial Statistics
JF - Spatial Statistics
SN - 2211-6753
M1 - 100448
ER -