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Uniform Confidence Bands for Infinite-Dimensional Partially Identified Parameters

Shunsuke Imai, Yuta Okamoto

arXiv 19 Jun 2026 · Econometrics

arXiv:2606.21224 · PDF · DOI · OpenAlex · Extracted main text

Abstract

Infinite-dimensional parameters are ubiquitous in empirical economics. This paper develops an Imbens--Manski--Stoye type confidence band for infinite-dimensional partially identified parameters. In particular, we propose multiplier bootstrap-based construction of a uniform confidence band. By employing approximation theorems for suprema of non-centered empirical processes indexed by possibly non-Donsker classes \citep{chernozhukov2016empirical}, we confirm the uniform validity of the proposed procedure.

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27
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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
1Chernozhukov, Victor and Chetverikov, Denis and Kato, Kengo (2016) Empirical and multiplier bootstraps for suprema of empirical processes of increasing complexity, and related Gaussian couplings1.000124100%
2Stoye, Jörg (2009) More on Confidence Intervals for Partially Identified Parameters1.000113100%
3Brigham R. Frandsen and Zachari A. Pond (2025) Simultaneous Confidence Intervals for Partially Identified Parameters1.00083100%
4Imbens, Guido W. and Manski, Charles F (2004) Confidence Intervals for Partially Identified Parameters0.69361100%
5Chernozhukov, Victor and Chetverikov, Denis and Kato, Kengo (2019) Inference on Causal and Structural Parameters using Many Moment Inequalities0.51121100%
6Heckman, James J. and Smith, Jeffrey and Clements, Nancy (1997) Making The Most Out Of Programme Evaluations and Social Experiments: Accounting For Heterogeneity in Programme Impacts0.51121100%
7Donald W.K. Andrews and Xiaoxia Shi (2014) Nonparametric inference based on conditional moment inequalities0.40511100%
8Andrews, Donald W. K. and Soares, Gustavo (2010) Inference for Parameters Defined by Moment Inequalities Using Generalized Moment Selection0.40511100%
9Otávio Bartalotti and Désiré Kédagni and Vitor Possebom (2023) Identifying marginal treatment effects in the presence of sample selection0.40511100%
10Arie Beresteanu and Yuya Sasaki (2021) Quantile regression with interval data0.40511100%

Showing the top 10 of 27 scored citations.