Uniformly valid confidence intervals post-model-selection

TL;DR

This paper introduces general methods for constructing confidence intervals that remain valid after model selection, accommodating misspecified models and data-driven procedures, with strong empirical performance.

Contribution

It develops a unified theoretical framework for uniformly valid post-model-selection confidence intervals applicable to various models and demonstrates their effectiveness through simulations.

Findings

Confidence intervals are valid regardless of model misspecification.

Proposed methods outperform existing tailored approaches in simulations.

Coverage guarantees hold for any data-driven model selection procedure.

Abstract

We suggest general methods to construct asymptotically uniformly valid confidence intervals post-model-selection. The constructions are based on principles recently proposed by Berk et al. (2013). In particular the candidate models used can be misspecified, the target of inference is model-specific, and coverage is guaranteed for any data-driven model selection procedure. After developing a general theory we apply our methods to practically important situations where the candidate set of models, from which a working model is selected, consists of fixed design homoskedastic or heteroskedastic linear models, or of binary regression models with general link functions. In an extensive simulation study, we find that the proposed confidence intervals perform remarkably well, even when compared to existing methods that are tailored only for specific model selection procedures.