Bootstrap consistency for general double/debiased machine learning estimators

2026-04-18

AI Summary

This work addresses the lack of theoretical justification for the widespread use of bootstrap inference with double/debiased machine learning (DML) estimators. It proposes a unified framework that integrates exchangeable weighted resampling, Neyman-orthogonal scores, and cross-fitting, and establishes—under the same conditions required for DML consistency—that the conditional distribution of the bootstrap approximates the sampling distribution of the original estimator in the sense of weak convergence. This result encompasses the classical Efron bootstrap as a special case. By rigorously validating bootstrap-based inference for DML, the paper provides the first formal theoretical foundation for this commonly employed practice, thereby filling a critical gap in the existing literature.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Multiagent Systems: Mechanism Design

Application Category

• Web Mining and Content Analysis: Machine learning and data science for the Web
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

Abstract

Double/debiased machine learning (DML) provides a general framework for inference with high-dimensional or otherwise complex nuisance parameters by combining Neyman-orthogonal scores with cross-fitting, thereby circumventing classical Donsker-type conditions in many modern machine-learning settings. Despite its strong empirical performance, bootstrap inference for DML estimators has received little theoretical justification. This is particularly noteworthy since bootstrap methods are suggested ad used for inference on DML estimators, even though bootstrap procedures can fail for estimators that are root-$n$ consistent and asymptotically normal. This paper fills this gap by establishing bootstrap validity for DML estimators under general exchangeably weighted resampling schemes, with Efron's bootstrap as a special case. Under exactly the same conditions required for the validity of DML itself, we prove that the bootstrap law converges conditionally weakly to the sampling law of the original estimator.

Problem

• double/debiased machine learning
• bootstrap consistency
• Neyman-orthogonal scores
• high-dimensional nuisance parameters
• exchangeably weighted resampling

Innovation

• double/debiased machine learning
• bootstrap consistency
• Neyman-orthogonal scores
• cross-fitting
• exchangeably weighted resampling