Bootstrap consistency for general double/debiased machine learning estimators
TLDR
This paper establishes the theoretical validity of bootstrap inference for Double/Debiased Machine Learning (DML) estimators, filling a critical gap.
Key contributions
- Proves bootstrap validity for DML estimators under general exchangeably weighted resampling schemes.
- Demonstrates conditional weak convergence of the bootstrap law to the sampling law of the estimator.
- Validates bootstrap under the exact same conditions required for DML estimator validity.
Why it matters
Bootstrap methods are widely applied for DML inference despite a lack of theoretical justification, which can lead to unreliable results. This paper provides the crucial theoretical foundation, enabling more robust and trustworthy statistical inference in complex, high-dimensional settings.
Original 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.
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