Uniform Confidence Bands for Infinite-Dimensional Partially Identified Parameters

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.