Nonparametric Instrumental Variable Analysis Without Structural Equations: Debiased Inference on Functionals of Inverse Problems with No Solutions
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Abstract (arXiv)
We consider debiased inference on finite-dimensional functionals of infinite-dimensional least-squares solutions to inverse problems as a way to avoid having to assume exact solutions exist. Such assumptions are substantive and not innocuous, and their failure may imperil inference when we impose them on the statistical model. Our approach instead allows us to conduct inference on a quantity that is defined regardless of solutions existing and coincides with the usual estimands when they do. For the case of instrumental variables, this means we can motivate the analysis with structural models but these do not need to hold exactly for the semiparametric inferential procedure to remain valid.
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References · 11
- 2019Orthogonal Statistical Learningcited by 151
- 2016Identifying Causal Effects With Proxy Variables of an Unmeasured Confoundercited by 139
- 2020Semiparametric proximal causal inferencecited by 59
- 2021Causal Inference Under Unmeasured Confounding With Negative Controls: A Minimax Learning Approachcited by 44
- 2015The Influence Function of Semiparametric Estimatorscited by 36
- 2024Applied Causal Inference Powered by ML and AIcited by 30
- 2022Inference on Strongly Identified Functionals of Weakly Identified Functionscited by 12
- 2023Source Condition Double Robust Inference on Functionals of Inverse Problemscited by 9
- 2025Nonparametric Instrumental Variable Inference with Many Weak Instrumentscited by 5
- 2025Nonparametric Instrumental Variable Regression with Observed Covariatescited by 5
- 2025The purpose of an estimator is what it does: Misspecification, estimands, and over-identificationcited by 1
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