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Asymmetric matrix-valued covariances for multivariate random fields on spheres


Alegría, Alfredo; Porcu, Emilio; Furrer, Reinhard (2018). Asymmetric matrix-valued covariances for multivariate random fields on spheres. Journal of Statistical Computation and Simulation, 88(10):1850-1862.

Abstract

Matrix-valued covariance functions are crucial to geostatistical modelling of multivariate spatial data. The classical assumption of symmetry of a multivariate covariance function is overly restrictive and has been considered as unrealistic for most of the real data applications. Despite of that, the literature on asymmetric covariance functions has been very sparse. In particular, there is some work related to asymmetric covariances on Euclidean spaces, depending on the Euclidean distance. However, for data collected over large portions of planet Earth, the most natural spatial domain is a sphere, with the corresponding geodesic distance being the natural metric. In this work, we propose a strategy based on spatial rotations to generate asymmetric covariances for multivariate random fields on the d-dimensional unit sphere. We illustrate through simulations as well as real data analysis that our proposal allows to achieve improvements in the predictive performance in comparison to the symmetric counterpart.

Abstract

Matrix-valued covariance functions are crucial to geostatistical modelling of multivariate spatial data. The classical assumption of symmetry of a multivariate covariance function is overly restrictive and has been considered as unrealistic for most of the real data applications. Despite of that, the literature on asymmetric covariance functions has been very sparse. In particular, there is some work related to asymmetric covariances on Euclidean spaces, depending on the Euclidean distance. However, for data collected over large portions of planet Earth, the most natural spatial domain is a sphere, with the corresponding geodesic distance being the natural metric. In this work, we propose a strategy based on spatial rotations to generate asymmetric covariances for multivariate random fields on the d-dimensional unit sphere. We illustrate through simulations as well as real data analysis that our proposal allows to achieve improvements in the predictive performance in comparison to the symmetric counterpart.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2018
Deposited On:18 Jan 2018 11:01
Last Modified:09 May 2018 01:01
Publisher:Taylor & Francis
ISSN:0094-9655
Funders:Schweizerischer Nationalfonds, Comisión Nacional de Investigación Científica y Tecnológica, Fondo Nacional de Desarrollo Científico y Tecnológico
OA Status:Green
Publisher DOI:https://doi.org/10.1080/00949655.2017.1406488

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