Extension of calibrated debiased machine learning (C-DML) to mixed-bias parameters

Establish whether the calibrated debiased machine learning (C-DML) framework for doubly robust asymptotically linear inference can be extended to handle general parameters characterized by the mixed bias property (as defined by Rotnitzky, Smucler, and Robins, 2021), beyond linear functionals of the outcome regression.

Background

The paper introduces calibrated debiased machine learning (C-DML), a unified and non-iterative framework that achieves doubly robust asymptotically linear inference for parameters that are linear functionals of the outcome regression. The main results show that C-DML remains asymptotically linear even when one nuisance function is estimated slowly or inconsistently, leveraging calibration to satisfy orthogonality conditions.

Rotnitzky, Smucler, and Robins (2021) characterize a broader class of estimands with the mixed bias property, where the bias decomposes into a product of nuisance errors. Extending C-DML beyond linear functionals to this broader class would generalize the applicability of doubly robust inference using black-box learners, but the authors indicate this extension is currently unresolved.