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Copulae on products of compact Riemannian manifolds

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Copulae on products of compact Riemannian manifolds. / Jupp, P.E.

In: Journal of Multivariate Analysis, Vol. 140, 09.2015, p. 92-98.

Research output: Contribution to journalArticle

Harvard

Jupp, PE 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

APA

Jupp, P. E. (2015). Copulae on products of compact Riemannian manifolds. Journal of Multivariate Analysis, 140, 92-98. https://doi.org/10.1016/j.jmva.2015.04.008

Vancouver

Jupp PE. Copulae on products of compact Riemannian manifolds. Journal of Multivariate Analysis. 2015 Sep;140:92-98. https://doi.org/10.1016/j.jmva.2015.04.008

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Jupp, P.E. / Copulae on products of compact Riemannian manifolds. In: Journal of Multivariate Analysis. 2015 ; Vol. 140. pp. 92-98.

Bibtex - Download

@article{f633416fa40947ec867dfc79dffdd159,
title = "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.",
keywords = "Uniform scores, Bivariate, Convolution, Homogeneous manifold, Markov process, Uniform distribution",
author = "P.E. Jupp",
year = "2015",
month = sep,
doi = "10.1016/j.jmva.2015.04.008",
language = "English",
volume = "140",
pages = "92--98",
journal = "Journal of Multivariate Analysis",
issn = "0047-259X",
publisher = "Academic Press Inc.",

}

RIS (suitable for import to EndNote) - Download

TY - JOUR

T1 - Copulae on products of compact Riemannian manifolds

AU - Jupp, P.E.

PY - 2015/9

Y1 - 2015/9

N2 - 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.

AB - 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.

KW - Uniform scores

KW - Bivariate

KW - Convolution

KW - Homogeneous manifold

KW - Markov process

KW - Uniform distribution

U2 - 10.1016/j.jmva.2015.04.008

DO - 10.1016/j.jmva.2015.04.008

M3 - Article

VL - 140

SP - 92

EP - 98

JO - Journal of Multivariate Analysis

JF - Journal of Multivariate Analysis

SN - 0047-259X

ER -

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