Debiased Machine Learning with Many Cross-Fitting Folds

Amilcar Velez

Papers from arXiv.org

Abstract: This paper studies debiased machine learning (DML) when the number of cross-fitting folds, $K_n$, may grow with the sample size $n$. Existing fixed-$K$ asymptotic theory implies that DML1 and DML2, the two main DML variants, are asymptotically equivalent, providing no guidance on which variant to use or how to choose $K_n$. We show that this equivalence can break down when $K_n$ grows proportionally to $\sqrt{n}$: DML1 can exhibit asymptotic bias, in which case standard inference based on DML1 fails---as can occur, for instance, for the local average treatment effect (LATE)---whereas inference based on DML2 remains valid. Moreover, we show that, under an algorithmic-stability condition, estimation and inference based on DML2 are valid for any $2\le K_n \le n$, including the leave-one-out case, $K_n=n$. Finally, for scalar DML2 estimators whose first-step estimators admit a stochastic linear expansion, we derive a second-order approximation showing that larger values of $K_n$ reduce the second-order asymptotic bias and mean-squared error, although the marginal improvements diminish.

Date: 2024-11, Revised 2026-08
New Economics Papers: this item is included in nep-big, nep-cmp, nep-ecm and nep-mac
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Citations: View citations in EconPapers (4)

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