Interpretability of Relative Smoothness Assumptions for CQTE

Determine a principled and precise interpretation of "relative smoothness" in the conditional quantile treatment effect (CQTE) compared to the individual conditional quantile functions as functions of covariates, so as to assess when and why assuming smoother CQTE than marginal quantiles is reasonable in heterogeneous treatment effect analysis.

Background

The paper contrasts estimation properties of CATE and CQTE, noting that CQTE often depends on the smoothness of marginal conditional quantile functions rather than the smoothness of the effect estimand itself. While CATE has well-developed theory and examples supporting assumptions of smoothness, analogous interpretability for CQTE is lacking.

The authors introduce the conditional quantile comparator (CQC) to address estimation challenges and interpretability gaps, but explicitly acknowledge that the literature does not clearly explain or justify the assumption that CQTE may be smoother than the individual conditional quantile functions. Clarifying this would inform modeling choices and theoretical guarantees for quantile-based treatment effect estimands.