Multivariate radial symmetry of copula functions: finite sample comparison in the i.i.d case

• Main Authors: Billio Monica, Frattarolo Lorenzo, Guégan Dominique
• Format: Article
• Language: English
• Published: De Gruyter 2021-05-01
• Series: Dependence Modeling
• Subjects: copula; reflection symmetry; radial symmetry; empirical process; 62g10; 62g30; 62h05; 62h15
• Online Access: https://doi.org/10.1515/demo-2021-0102

Given a d-dimensional random vector X = (X1, . . ., Xd), if the standard uniform vector U obtained by the component-wise probability integral transform (PIT) of X has the same distribution of its point reflection through the center of the unit hypercube, then X is said to have copula radial symmetry. We generalize to higher dimensions the bivariate test introduced in [11], using three different possibilities for estimating copula derivatives under the null. In a comprehensive simulation study, we assess the finite-sample properties of the resulting tests, comparing them with the finite-sample performance of the multivariate competitors introduced in [17] and [1].