Valid Post-Selection Inference

• Activity Number: 39
• Type: Contributed
• Date/Time: Sunday, July 31, 2011 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Kai Zhang*+ and Richard Berk and Lawrence Brown and Andreas Buja and Linda Zhao
• Companies: University of Pennsylvania and University of Pennsylvania and University of Pennsylvania and University of Pennsylvania and University of Pennsylvania
• Keywords: Statistical Inference ; Model Selection ; Simultaneity

Abstract

It is common practice in statistical data analysis to perform data-driven model selection and derive statistical inference from the selected model. Such inference is generally invalid. We propose to produce valid "post-selection inference" by reducing the problem to one of simultaneous inference. Simultaneity is required for all linear functions that arise as coefficient estimates in all submodels. By purchasing "simultaneity insurance" for all possible submodels, the resulting post-selection inference is rendered universally valid under all possible model selection procedures. This inference is therefore generally conservative for particular selection procedures, but it is always less conservative than full Scheffe protection. We describe the structure of the simultaneous inference problem and give some asymptotic results.