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Strictly positive definite multivariate covariance functions on spheres

Lookup NU author(s): Professor Emilio Porcu

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Abstract

© 2018 Elsevier Inc. 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.

Publication metadata

Author(s): Guella JC, Menegatto VA, Porcu E

Publication type: Article

Publication status: Published

Journal: Journal of Multivariate Analysis

Year: 2018

Volume: 166

Pages: 150-159

Print publication date: 01/07/2018

Online publication date: 10/03/2018

Acceptance date: 14/08/2017

Date deposited: 05/06/2018

ISSN (print): 0047-259X

ISSN (electronic): 1095-7243

Publisher: Academic Press Inc.

URL: https://doi.org/10.1016/j.jmva.2018.03.001

DOI: 10.1016/j.jmva.2018.03.001

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