Finite-sample theory for mean/median aggregation of DML across sample splits

Determine whether aggregating double/debiased machine learning estimators across multiple random sample splits using mean or median aggregation improves finite-sample performance relative to using a single cross-fitted DML estimator, and, if so, establish formal theoretical guarantees quantifying any improvement under standard conditions on nuisance-function estimation and sample splitting.

Background

The paper highlights that cross-fitting introduces randomness through the choice of sample partitions, which can lead to noticeable finite-sample variability, especially in smaller samples typical of staggered-adoption designs. To summarize results across different random splits, the authors suggest median aggregation of DML estimates and note that such aggregated estimators are first-order equivalent to any single-split DML estimator.

Despite this practical recommendation, the authors explicitly state that they are not aware of formal theoretical arguments demonstrating improved finite-sample properties of mean or median aggregation. This leaves open whether aggregation across splits offers a provable finite-sample advantage and under what conditions. While higher-order analysis has provided guidance on the number of folds in some settings, a theoretical foundation for aggregation itself remains missing.