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I propose a new type of confidence interval for correct asymptotic inferenceafter using data to select a model of interest without assuming any model iscorrectly specified. This hybrid confidence interval is constructed bycombining techniques from the selective inference and post-selection inferenceliteratures to yield a short confidence interval across a wide range of datarealizations. I show that hybrid confidence intervals have correct asymptoticcoverage, uniformly over a large class of probability distributions that do notbound scaled model parameters. I illustrate the use of these confidenceintervals in the problem of inference after using the LASSO objective functionto select a regression model of interest and provide evidence of theirdesirable length and coverage properties in small samples via a set of MonteCarlo experiments that entail a variety of different data distributions as wellas an empirical application to the predictors of diabetes disease progression.

Hybrid Confidence Intervals for Informative Uniform Asymptotic Inference After Model Selection