Copula-based measures and tests for conditional asymmetry

Abstract

In this paper, we develop copula-based measures and testing procedures for the conditional asymmetry of a random variable given another. The resulting tests are ranked based and thus robust to the outliers. The asymptotic properties of the test statistics are investigated. Simulation studies and real data analysis are conducted to illustrate the performance of the proposed tests.

Keywords:

• Bivariate symmetry
• Conditional symmetry
• Copula
• Test

Acknowledgements

The authors would like to thank the Editor and the two anonymous reviewers for their insightful comments on the earlier version of this paper which led to significant improvement.