Bootstrap consistency for general double/debiased machine learning estimators

TL;DR

This paper establishes the theoretical validity of bootstrap methods for double/debiased machine learning estimators, ensuring reliable inference in high-dimensional and complex models.

Contribution

It provides the first rigorous proof of bootstrap consistency for DML estimators under general resampling schemes, including Efron's bootstrap.

Findings

Bootstrap law converges conditionally weakly to the sampling law of DML estimators.

Validity of bootstrap is proven under the same conditions as DML itself.

Applicable to a wide range of resampling schemes beyond Efron's bootstrap.

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.