Hybrid Confidence Intervals for Informative Uniform Asymptotic Inference After Model Selection

TL;DR

This paper introduces a new hybrid confidence interval method for valid post-model-selection inference that maintains correct coverage and is applicable across diverse data distributions, demonstrated through simulations and real data.

Contribution

It develops a novel hybrid confidence interval combining selective and post-selection inference techniques, applicable without assuming correct model specification.

Findings

Correct asymptotic coverage across various distributions

Shorter confidence intervals compared to existing methods

Effective in small samples and real data applications

Abstract

I propose a new type of confidence interval for correct asymptotic inference after using data to select a model of interest without assuming any model is correctly specified. This hybrid confidence interval is constructed by combining techniques from the selective inference and post-selection inference literatures to yield a short confidence interval across a wide range of data realizations. I show that hybrid confidence intervals have correct asymptotic coverage, uniformly over a large class of probability distributions that do not bound scaled model parameters. I illustrate the use of these confidence intervals in the problem of inference after using the LASSO objective function to select a regression model of interest and provide evidence of their desirable length and coverage properties in small samples via a set of Monte Carlo experiments that entail a variety of different data distributions as well as an empirical application to the predictors of diabetes disease progression.