On the asymptotic validity of confidence sets for linear functionals of solutions to integral equations.

ABSTRACT: This paper examines the construction of confidence sets for parameters defined as linear functionals of a function of [Formula: see text] and [Formula: see text] whose conditional mean given [Formula: see text] and [Formula: see text] equals the conditional mean of another variable [Formula: see text] given [Formula: see text] and [Formula: see text]. Many estimands of interest in causal inference can be expressed in this form, including the average treatment effect in proximal causal inference and treatment effect contrasts in instrumental variable models. We derive a necessary condition for a confidence set to be uniformly valid over a model that allows for the dependence between [Formula: see text] and [Formula: see text] given [Formula: see text] to be arbitrarily weak. We show that, f

SUBMITTER: Smucler E 

PROVIDER: S-EPMC12614171 | biostudies-literature | 2025

REPOSITORIES: biostudies-literature