45: Exact Confidence Intervals for Randomization-Based Inference

Music City Center 

Permutation tests provide exact finite-sample inference under minimal assumptions, making them invaluable for analyzing experimental data. Though these tests are widely used for hypothesis testing, existing methods for inverting them to obtain confidence intervals have focused largely on location-scale models, leaving a gap in our ability to construct exact, randomization-based confidence intervals for many common outcome models. In this paper, we present a new approach to inverting permutation tests applicable to a broad class of outcome types, such as binary, count, heavy-tailed, and censored outcomes, with natural extensions to common semiparametric models, such as the logistic partially linear model. Importantly, our method is computationally efficient, requiring only a one-dimensional grid search across the real line, while related approaches are generally more computationally intensive and conservative. Through an extensive simulation study, we demonstrate the efficacy of our confidence interval construction across diverse outcome types in both parametric and semiparametric settings.

Randomization testing

Exact confidence intervals

Semiparametric inference

Finite-sample inference 

Section on Statistical Learning and Data Science