Debiased Machine Learning: Identification, Estimation, and Shape Constraints
Qihui Chen, Ka Yan Cheng, Zheng Fang
econ.EM, math.ST, stat.ME, stat.ML
Submitted: 2026-07-27
License: http://creativecommons.org/licenses/by/4.0/
The gist: We develop a general framework of identification and estimation for automatic debiased machine learning (DML) where the parameter of interest theta 0 is identified by a moment condition involving a
Terminology
Abstract
We develop a general framework of identification and estimation for automatic debiased machine learning (DML) where the parameter of interest theta 0 is identified by a moment condition involving a nuisance gamma 0 that may be high dimensional. We establish conditions under which the Riesz representer alpha 0, which is at the core of DML, is identified, and show that the identification occurs precisely when alpha 0 uniquely optimizes a quadratic functional. This characterization enables us to develop a general estimation procedure for alpha 0 that allows for generic gamma 0 including those defined by models with endogeneity and encompasses both classical sieves and modern architectures such as deep neural networks. To improve estimation precision and mitigate the curse of dimensionality, we incorporate shape constraints on gamma 0 by embedding them into a possibly nonlinear parameter space. We illustrate our estimation procedure through simulations and empirical applications.
Sources
- An Introduction to Double/Debiased Machine Learning
- Penalized GMM Framework for Inference on Functionals of Nonparametric Instrumental Variable Estimators
- Adversarial Estimation of Riesz Representers
- Automatic Debiased Machine Learning via Riesz Regression
- Automatic Locally Robust GMM with Machine-Learning-Generated Regressors
- A Unifying Framework for Testing Shape Restrictions
- Kernel Ridge Riesz Representers: Generalization, Mis-specification, and the Counterfactual Effective Dimension
- Automatic Debiased Machine Learning for Smooth Functionals of Nonparametric M-Estimands
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