Finite Sample Inference in Incomplete Models

TL;DR

This paper introduces a method for constructing confidence regions in incomplete models that guarantees exact finite-sample coverage, utilizing optimal transport and linear programming techniques.

Contribution

It develops a novel test-based approach for finite-sample inference in incomplete models, extending Monte Carlo tests with a new optimal transport characterization.

Findings

Confidence regions with exact finite-sample coverage.

Use of discrete optimal transport and linear programming for computation.

A fast preliminary search method with a conservative test.

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.