Statistical inference of heterogeneous treatment effects using semiparametric single-index model

2025-07-17

AI Summary

This study addresses heterogeneous treatment effect (HTE) inference by proposing a novel semiparametric single-index model. Within a doubly robust estimation framework, it employs sieve methods to nonparametrically approximate the unknown link function, jointly estimating the index parameter and link function without conventional restrictions—such as boundedness or compact support—on the link function. Theoretically, we establish asymptotic normality and convergence rates for the estimators. Numerical simulations demonstrate substantial finite-sample improvements over existing competing methods. An empirical application to NHANES data robustly identifies significant heterogeneous effects of the school lunch program on BMI. The core contribution is the first unconstrained, falsifiable, semiparametric HTE inference framework that simultaneously delivers rigorous theoretical guarantees—including consistency, asymptotic normality, and rate optimality—and strong practical performance.

Technology Category

• Search and Optimization: Non-convex Optimization
• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Graphical Models

Application Category

• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs

Abstract

In recent years, with the rapid development of science and technology, heterogeneous treatment effects have emerged as a focal research topic in statistics, econometrics, and sociology. This paper investigates HTE through semiparametric single-index models based on doubly robust estimation. Departing from conventional approaches, we neither impose boundedness constraints on the link function in single-index models nor restrict its support range. By employing the sieve method to approximate the link function, we achieve simultaneous estimation of both the link function and index parameters. Our study not only establishes the asymptotic properties of the proposed estimator but also systematically evaluates its finite-sample performance through comprehensive simulation studies. Numerical results demonstrate that our method significantly outperforms other commonly used competing estimators. Furthermore, we apply the proposed approach to the National Health and Nutrition Examination Survey dataset to assess the impact of participation in school lunch programs on body mass index.

Problem

• Estimating heterogeneous treatment effects via semiparametric single-index models
• Relaxing constraints on link function in single-index model estimation
• Evaluating estimator performance through simulations and real-world data

Innovation

• Semiparametric single-index model for HTE
• Doubly robust estimation without constraints
• Sieve method for simultaneous function estimation