A1810
Title: On the asymptotic properties of debiased machine learning estimators
Authors: Amilcar Velez - Cornell University (United States) [presenting]
Abstract: Debiased machine learning (DML) is considered 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, two variants of DML estimators, are asymptotically equivalent, providing no guidance on which variant to use or how to choose $K_n$. It is shown that when $K_n \to \sqrt{n}$, DML1 can exhibit asymptotic bias, implying that standard inference based on DML1 may fail, whereas inference based on DML2 remains valid. Under an algorithm stability condition, the standard asymptotic theory for DML2 remains valid for any $K_n \le n$. Finally, for scalar DML2 estimators whose first-step estimators admit a linear stochastic expansion, a valid second-order asymptotic approximation is derived showing that larger $K_n$ lowers second-order asymptotic bias and mean-squared error, although the marginal improvements decline with $K_n$. In particular, among common choices for DML2, $K_n=10$ is preferred over $K_n=5$.
