Hybrid confidence intervals for informative uniform asymptotic inference after model selection

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.

Automated summary

I propose a new type of confidence interval that allows correct asymptotic inference after model selection without assuming any model is correctly specified. This hybrid confidence interval combines techniques from selective inference and post-selection inference to provide a short interval across various data realizations. The results show that hybrid confidence intervals have correct asymptotic coverage over a broad class of probability distributions with no bound on scaled model parameters. Monte Carlo experiments and an empirical application on diabetes disease progression predictors demonstrate the desirable length and coverage properties of these confidence intervals in small samples.