Data-Driven Uniform Inference for General Continuous Treatment Models via Minimum-Variance Weighting

2026-02-02

AI Summary

This study addresses the challenge of constructing valid confidence intervals for nonparametric estimation of generalized dose-response functions (GDRFs) in the presence of confounding variables. The authors propose a weighted local linear regression approach that employs closed-form minimum-variance stabilized weights to effectively remove empirical associations between the treatment and confounders. A uniform confidence band is constructed via the bootstrap, and a uniform Bahadur representation of the estimator is established, enabling fully data-driven undersmoothing and bias correction. Theoretical analysis confirms the asymptotic validity of the proposed confidence bands, while simulations and empirical applications demonstrate substantial improvements over existing methods in both estimation accuracy and inferential reliability.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Graphical Models
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Ai et al. (2021) studied the estimation of a general dose-response function (GDRF) of a continuous treatment that includes the average dose-response function, the quantile dose-response function, and other expectiles of the dose-response distribution. They specified the GDRF as a parametric function of the treatment status only and proposed a weighted regression with the weighting function estimated using the maximum entropy approach. This paper specifies the GDRF as a nonparametric function of the treatment status, proposes a weighted local linear regression for estimating GDRF, and develops a bootstrap procedure for constructing the uniform confidence bands. We propose stable weights with minimum sample variance while eliminating the sample association between the treatment and the confounding variables. The proposed weights admit a closed-form expression, allowing them to be computed efficiently in the bootstrap sampling. Under certain conditions, we derive the uniform Bahadur representation for the proposed estimator of GDRF and establish the validity of the corresponding uniform confidence bands. A fully data-driven approach to choosing the undersmooth tuning parameters and a data-driven bias-control confidence band are included. A simulation study and an application demonstrate the usefulness of the proposed approach.

Problem

• continuous treatment
• dose-response function
• uniform inference
• confounding variables
• nonparametric estimation

Innovation

• minimum-variance weighting
• nonparametric dose-response function
• uniform confidence bands
• bootstrap inference
• data-driven tuning