Copulae on products of compact Riemannian manifolds
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Abstract One standard way of considering a probability distribution on the unit n -cube, [0 , 1]n , due to Sklar (1959), is to decompose it into its marginal distributions and a copula, i.e. a probability distribution on [0 , 1]n with uniform marginals. The definition of copula was extended by Jones et al. (2014) to probability distributions on products of circles. This paper defines a copula as a probability distribution on a product of compact Riemannian manifolds that has uniform marginals. Basic properties of such copulae are established. Two fairly general constructions of copulae on products of compact homogeneous manifolds are given; one is based on convolution in the isometry group, the other using equivariant functions from compact Riemannian manifolds to their spaces of square integrable functions. Examples illustrate the use of copulae to analyse bivariate spherical data and bivariate rotational data.
Jupp , P E 2015 , ' Copulae on products of compact Riemannian manifolds ' Journal of Multivariate Analysis , vol. 140 , pp. 92-98 . DOI: 10.1016/j.jmva.2015.04.008
Journal of Multivariate Analysis
Copyright © 2015 Published by Elsevier Inc. This work is made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at http://dx.doi.org/10.1016/j.jmva.2015.04.008
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