Optimal finite sample post-selection confidence distributions in generalized linear models

Abstract

Uniformly most powerful confidence distributions are obtained for parameters in selected models of the exponential family. A conditioning on the selection event as well as on the sufficient statistics of nuisance parameters guarantees valid post-selection inference. Optimal confidence intervals are obtained directly from the confidence distribution without requiring an inversion of pivotal quantities. Simulations showcase that the method works also when all models are misspecified.