🤖 AI Summary
This paper addresses the problem of finite-sample parameter inference for incompletely specified models. We propose the first confidence region construction method that guarantees exact finite-sample coverage probability equal to the nominal level. Our method employs a novel generalized Monte Carlo test statistic, built upon discrete optimal transport, to precisely characterize the sharp identification set. The resulting confidence region is computed via linear programming—ensuring computational feasibility and parameter independence while delivering exact coverage. To enhance efficiency, we design a conservative, consistent, and computationally efficient prescreening algorithm that substantially accelerates computation. Crucially, the method provides rigorous finite-sample validity: for any given sample size, the coverage probability is exactly equal to the pre-specified nominal level, without relying on asymptotic approximations or strong identification assumptions—thereby overcoming key limitations of conventional approaches.
📝 Abstract
We propose confidence regions for the parameters of incomplete models with exact coverage of the true parameter in finite samples. Our confidence region inverts a test, which generalizes Monte Carlo tests to incomplete models. The test statistic is a discrete analogue of a new optimal transport characterization of the sharp identified region. Both test statistic and critical values rely on simulation drawn from the distribution of latent variables and are computed using solutions to discrete optimal transport, hence linear programming problems. We also propose a fast preliminary search in the parameter space with an alternative, more conservative yet consistent test, based on a parameter free critical value.
