Copulae on products of compact Riemannian manifolds
Abstract
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.
Citation
Jupp , P E 2015 , ' Copulae on products of compact Riemannian manifolds ' , Journal of Multivariate Analysis , vol. 140 , pp. 92-98 . https://doi.org/10.1016/j.jmva.2015.04.008
Publication
Journal of Multivariate Analysis
Status
Peer reviewed
ISSN
0047-259XType
Journal article
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