A measure of radial asymmetry for bivariate copulas based on Sobolev norm

Abstract

The modified Sobolev norm is used to construct an index for measuring the degree of radial asymmetry of a copula. We study various aspects of this index and discuss its rank-based estimator. Through simulation and a real data example, we compare the proposed index with the other radial asymmetry measures.

Keywords

• Bivariate symmetry,Copula,Empirical process,Radial asymmetry,Sobolev norm

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