Exact post-selection inference, with application to the lasso

We develop a framework for inference after model selection based on the Lasso. At the core of this framework is a result that characterizes the exact (non-asymptotic) distribution of a pivot computed from the Lasso solution. This pivot allows us to (i) devise a test statistic that has an exact (non-asymptotic) $\unif(0,1)$ distribution under the null hypothesis that all relevant variables have been included in the model, and (ii) construct valid confidence intervals for the selected coefficients that account for the selection procedure.