Uniform Confidence Bands for Infinite-Dimensional Partially Identified Parameters

Shunsuke Imai and Yuta Okamoto

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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.

Date: 2026-06, Revised 2026-07
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