Valid confidence intervals for post-model-selection predictors

TL;DR

This paper extends the PoSI confidence intervals to provide valid inference for predictors after model selection in linear regression, ensuring coverage regardless of the selection method used.

Contribution

The authors generalize PoSI intervals to cover post-model-selection predictors, enhancing inference validity in linear regression models.

Findings

PoSI intervals guarantee coverage for post-model-selection predictors.

The method is model-agnostic, independent of selection procedure.

The approach improves reliability of inference after model selection.

Abstract

We consider inference post-model-selection in linear regression. In this setting, Berk et al.(2013) recently introduced a class of confidence sets, the so-called PoSI intervals, that cover a certain non-standard quantity of interest with a user-specified minimal coverage probability, irrespective of the model selection procedure that is being used. In this paper, we generalize the PoSI intervals to post-model-selection predictors.