Analysis of directional dependence using asymmetric copula-based regression models

The directional dependence between variables using asymmetric copula regression has drawn much attention in recent years. There are, however, some critical issues which have not been properly addressed in regards to the statistical inference of the directional dependence. For example, the previous use of asymmetric copulas failed to fully capture the dependence patterns between variables, and the method used for the parameter estimation was not optimal. In addition, no method was considered for selecting a suitable asymmetric copula or for computing the general measurements of the directional dependence when there are no closed-form expressions. In this paper, we propose a generalized multiple-step procedure for the full inference of the directional dependence in joint behaviour based on the asymmetric copula regression. The proposed procedure utilizes several novel methodologies that have not been considered in the literature of the analysis of directional dependence. The performance and advantages of the proposed procedure are illustrated using two real data examples, one from biological research on histone genes, and the other from developmental research on attention deficit hyperactivity disorder.