Quantile Association Regression Models

Abstract

It is often important to study the association between two continuous variables. In this work, we propose a novel regression framework for assessing conditional associations on quantiles. We develop general methodology which permits covariate effects on both the marginal quantile models for the two variables and their quantile associations. The proposed quantile copula models have straightforward interpretation, facilitating a comprehensive view of association structure which is much richer than that based on standard product moment and rank correlations. We show that the resulting estimators are uniformly consistent and weakly convergent as a process of the quantile index. Simple variance estimators are presented which perform well in numerical studies. Extensive simulations and a real data example demonstrate the practical utility of the methodology. Supplementary materials for this article are available online.

KEY WORDS:

• Conditional association
• Copula
• Hypothesis testing
• Induced smoothing
• Odds ratio
• Varying coefficient