On the monotonicity of copula-based conditional distributions

TL;DR

This paper establishes conditions under which copula-based conditional distributions are stochastically ordered, ensuring monotonicity of conditional means and quantiles with respect to covariates, independent of marginal distributions.

Contribution

It provides necessary and sufficient conditions for the monotonicity of copula-based conditional distributions, independent of marginals.

Findings

Conditions for stochastic ordering of conditional distributions

Monotonicity of conditional mean and quantiles

Applicability regardless of marginal distributions

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.