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Inference on Strongly Identified Functionals of Weakly Identified Functions

Andrew Bennett, Nathan Kallus, Xiaojie Mao, Whitney Newey, Vasilis Syrgkanis, Masatoshi Uehara

arXiv 17 Aug 2022 · Statistics — Methodology · publishedJournal of the Royal Statistical Society Series B (Statistical Methodology) (2025) · 2 citations (OpenAlex)

arXiv:2208.08291 · PDF · DOI · OpenAlex · Extracted main text

Abstract

In a variety of applications, including nonparametric instrumental variable (NPIV) analysis, proximal causal inference under unmeasured confounding, and missing-not-at-random data with shadow variables, we are interested in inference on a continuous linear functional (e.g., average causal effects) of nuisance function (e.g., NPIV regression) defined by conditional moment restrictions. These nuisance functions are generally weakly identified, in that the conditional moment restrictions can be severely ill-posed as well as admit multiple solutions. This is sometimes resolved by imposing strong conditions that imply the function can be estimated at rates that make inference on the functional possible. In this paper, we study a novel condition for the functional to be strongly identified even when the nuisance function is not; that is, the functional is amenable to asymptotically-normal estimation at $\sqrt{n}$-rates. The condition implies the existence of debiasing nuisance functions, and we propose penalized minimax estimators for both the primary and debiasing nuisance functions. The proposed nuisance estimators can accommodate flexible function classes, and importantly they can converge to fixed limits determined by the penalization regardless of the identifiability of the nuisances. We use the penalized nuisance estimators to form a debiased estimator for the functional of interest and prove its asymptotic normality under generic high-level conditions, which provide for asymptotically valid confidence intervals. We also illustrate our method in a novel partially linear proximal causal inference problem and a partially linear instrumental variable regression problem.

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106
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272
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106
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30
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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Nathan Kallus, Xiaojie Mao, and Masatoshi Uehara (2021) Causal inference under unmeasured confounding with negative controls: A minimax learning approach, 2021 self1.000167100%
2Qihui Chen (2021) Robust and optimal estimation for partially linear instrumental variables models with partial identification1.000154100%
3Nishanth Dikkala, Greg Lewis, Lester Mackey, and Vasilis Syrgkanis (2020) Minimax estimation of conditional moment models self1.00083100%
4Thomas A Severini and Gautam Tripathi (2012) Efficiency bounds for estimating linear functionals of nonparametric regression models with endogenous regressors1.00075100%
5Wei Li, Wang Miao, and Eric Tchetgen Tchetgen (2022) Nonparametric inference about mean functionals of nonignorable nonresponse data without identifying the joint distribution1.00074100%
6Victor Chernozhukov, Denis Chetverikov, Mert Demirer, Esther Duflo,… (2018) Double/debiased machine learning for treatment and structural parameters self1.00074100%
7Marine Carrasco, jean-pierre Florens, and Eric Renault (2007) Chapter 77 linear inverse problems in structural econometrics estimation based on spectral decomposition and regularization1.00053100%
8Yifan Cui, Hongming Pu, Xu Shi, Wang Miao, and Eric Tchetgen Tchetgen (2022) Semiparametric proximal causal inference0.96911691%
9Wang Miao and Eric Tchetgen Tchetgen (2018) A confounding bridge approach for double negative control inference on causal effects (supplement and sample codes are included)0.92844100%
10AmirEmad Ghassami, Andrew Ying, Ilya Shpitser, and Eric Tchetgen Tch… (2021) Minimax kernel machine learning for a class of doubly robust functionals0.92843100%

Showing the top 10 of 106 scored citations.

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