Direct Doubly Robust Estimation of Conditional Quantile Contrasts

2026-01-27

AI Summary

This work proposes the first direct estimation framework for conditional quantile contrast (CQC), circumventing the conventional indirect approach that relies on estimating the difference of conditional cumulative distribution functions followed by inversion—a procedure often opaque and difficult to interpret. By explicitly parameterizing and modeling the CQC itself, the proposed method enhances interpretability and naturally accommodates prior constraints. It enjoys double robustness, with estimation error complexity depending solely on the CQC function. Both theoretical analysis and empirical evaluations demonstrate superior estimation accuracy over existing methods across diverse simulated settings and real-world data, including a job training program. Notably, the approach reveals that as participant age increases, the range of potential income gains narrows, offering new substantive insights.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Stochastic Optimization
• Intelligent Robots: State Estimation

Application Category

• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

Within heterogeneous treatment effect (HTE) analysis, various estimands have been proposed to capture the effect of a treatment conditional on covariates. Recently, the conditional quantile comparator (CQC) has emerged as a promising estimand, offering quantile-level summaries akin to the conditional quantile treatment effect (CQTE) while preserving some interpretability of the conditional average treatment effect (CATE). It achieves this by summarising the treated response conditional on both the covariates and the untreated response. Despite these desirable properties, the CQC's current estimation is limited by the need to first estimate the difference in conditional cumulative distribution functions and then invert it. This inversion obscures the CQC estimate, hampering our ability to both model and interpret it. To address this, we propose the first direct estimator of the CQC, allowing for explicit modelling and parameterisation. This explicit parameterisation enables better interpretation of our estimate while also providing a means to constrain and inform the model. We show, both theoretically and empirically, that our estimation error depends directly on the complexity of the CQC itself, improving upon the existing estimation procedure. Furthermore, it retains the desirable double robustness property with respect to nuisance parameter estimation. We further show our method to outperform existing procedures in estimation accuracy across multiple data scenarios while varying sample size and nuisance error. Finally, we apply it to real-world data from an employment scheme, uncovering a reduced range of potential earnings improvement as participant age increases.

Problem

• Conditional Quantile Comparator
• Heterogeneous Treatment Effect
• Estimation Inversion
• Double Robustness
• Conditional Quantile Treatment Effect

Innovation

• direct estimation
• conditional quantile comparator
• double robustness
• heterogeneous treatment effect
• quantile treatment effect