On the monotonicity of copula-based conditional distributions

2019/01/31 by Nasri, Bouchra R., Remillard, Bruno N.
#FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1902.00050

Abstract

In this paper, we find necessary and sufficient conditions so that copula-based conditional distributions of a response variable with respect to covariates, are ordered with respect to the simple stochastic order introduced by Lehmann. These conditions do not depend on the marginal distributions of the random variables. As a result, we have conditions to ensure that the conditional mean and conditional quantiles are monotonic with respect to the covariates.

Related

• Modeling directional monotonicity with copulas
• Copula representations and order statistics for conditionally independent random variables
• Conditional copula representations and extremal bounds for multivariate statistical functionals
• Copulas from Order Statistics
• Dependence properties of bivariate copula families