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Strictly positive definite multivariate covariance functions on spheres

Jean Carlo Guella, Valdir Antonio Menegatto and Emilio Porcu

Journal of Multivariate Analysis, 2018, vol. 166, issue C, 150-159

Abstract: We study the strict positive definiteness of matrix-valued covariance functions associated to multivariate random fields defined over d-dimensional spheres of the (d+1)-dimensional Euclidean space. Characterization of strict positive definiteness is crucial to both estimation and cokriging prediction in classical geostatistical routines. We provide characterization theorems for high dimensional spheres as well as for the Hilbert sphere. We offer a necessary condition for positive definiteness on the circle. Finally, we discuss a parametric example which might turn to be useful for geostatistical applications.

Keywords: Covariance functions; Isotropy; Spheres; Strictly positive definite (search for similar items in EconPapers)
Date: 2018
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Handle: RePEc:eee:jmvana:v:166:y:2018:i:c:p:150-159