Adaptive Estimation and Inference in Conditional Moment Models via the Discrepancy Principle
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866912935111032832 |
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| author | Tan, Jiyuan Syrgkanis, Vasilis |
| author_facet | Tan, Jiyuan Syrgkanis, Vasilis |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_01337 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Adaptive Estimation and Inference in Conditional Moment Models via the Discrepancy Principle Tan, Jiyuan Syrgkanis, Vasilis Machine Learning 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. |
| title | Adaptive Estimation and Inference in Conditional Moment Models via the Discrepancy Principle |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2603.01337 |