Exact uniformly most powerful post‐selection confidence distributions

A conditioning on the event of having selected one model from a set of possibly misspecified normal linear regression models, leads to the construction of uniformly optimal conditional confidence distributions. They can be used for valid post-selection inference. The constructed conditional confidence distributions are finite sample exact and encompass all information regarding the focus parameter in the selected model. This includes the construction of optimal post-selection confidence intervals at all significance levels and uniformly most powerful hypothesis tests.