  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.
