Adaptive Estimation and Inference in Conditional Moment Models via the Discrepancy Principle
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Abstract (arXiv)
We study adaptive estimation and inference in ill-posed linear inverse problems defined by conditional moment restrictions. Existing regularized estimators such as Regularized DeepIV (RDIV) require prior knowledge of the smoothness of the nuisance function, typically encoded by a beta source condition to tune their regularization parameters. In practice, this smoothness is unknown, and misspecified hyperparameters can lead to suboptimal convergence or instability. We introduce a discrepancy-principle-based framework for adaptive hyperparameter selection that automatically balances bias and variance without relying on the unknown smoothness parameter. Our framework applies to both RDIV (Li et al. [2024]) and the Tikhonov Regularized Adversarial Estimator (TRAE) (Bennett et al. [2023a]) and achieves the same rates in both weak and strong metrics. Building on this, we construct a fully adaptive doubly robust estimator for linear functionals that attains the optimal rate of the better-conditioned primal or dual problem, providing a practical, theoretically grounded approach for adaptive inference in ill-posed econometric models.
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References · 16
- 2019Orthogonal Statistical Learningcited by 150
- 2019Kernel Instrumental Variable Regressioncited by 118
- 2020An Introduction to Proximal Causal Learningcited by 91
- 2020Minimax Estimation of Conditional Moment Modelscited by 83
- 2020Semiparametric proximal causal inferencecited by 58
- 2021Causal Inference Under Unmeasured Confounding With Negative Controls: A Minimax Learning Approachcited by 43
- 2021Deep Proxy Causal Learning and its Application to Confounded Bandit Policy Evaluationcited by 39
- 2018A confounding bridge approach for double negative control inference on causal effectscited by 36
- 2018Adversarial Generalized Method of Momentscited by 34
- 2020Provably Efficient Neural Estimation of Structural Equation Model: An Adversarial Approachcited by 31
- 2020The Variational Method of Momentscited by 23
- 2020Instrumental Variable Regression via Kernel Maximum Moment Losscited by 14
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- 2022Inference on Strongly Identified Functionals of Weakly Identified Functionscited by 12
- 2023Source Condition Double Robust Inference on Functionals of Inverse Problemscited by 8
- 2024Regularized DeepIV with Model Selectioncited by 6
- 2021Nonparametric inference about mean functionals of nonignorable nonresponse data without identifying the joint distributioncited by 4
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