@article{d3b6bb2dfedc422db1b544a50e39d20f,
title = "A catalogue of nonseparable positive semidefinite kernels on the product of two spheres",
abstract = "We present a catalogue of 26 parametric families of matrix-valued positive semidefinite kernels for modeling the spatial correlation structure of vector random fields defined over the product of two hyperspheres. Such a geometry has been proved successful to account for complex sources of seasonality and direction-dependence of phenomena regionalized on a large portion of planet Earth. All the kernels are nonseparable, as they cannot be written as the product of positive semidefinite kernels defined on hyperspheres, and sufficient validity conditions on their parameters are identified. Their analytical spectral representations and a spectral simulation algorithm are also provided. A side product is the derivation of new matrix-valued isotropic covariance kernels on hyperspheres, together with their analytical spectral representations.",
keywords = "Hypertorus, Matrix-valued covariance kernels, Schoenberg sequences, Space-time random fields, Spectral simulation",
author = "Xavier Emery and Peron, {Ana Paula} and Emilio Porcu",
note = "Funding Information: The first author acknowledges funding of the National Agency for Research and Development of Chile, through Grants ANID / FONDECYT / REGULAR / 1210050 and ANID PIA AFB220002. The second author acknowledges funding of FAPESP, Grant # 2021/04269-0, Brazil. Emilio Porcu is supported by FSU-2021-016 from Khalifa University of Science and Technology. Funding Information: This work was supported by the National Agency for Research and Development of Chile [grants ANID/FONDECYT/REGULAR/No. 1210050 and ANID PIA AFB220002], FAPESP, Brazil [grant 2021/04269-0] and Khalifa University of Science and Technology [grant FSU-2021-016]. The authors acknowledge two anonymous reviewers for their constructive comments. Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.",
year = "2022",
doi = "10.1007/s00477-022-02347-3",
language = "British English",
journal = "Stochastic Environmental Research and Risk Assessment",
issn = "1436-3240",
publisher = "Springer Science and Business Media Deutschland GmbH",
}