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Activity Number: 465
Type: Invited
Date/Time: Wednesday, August 12, 2015 : 8:30 AM to 10:20 AM
Sponsor: IMS
Abstract #314443
Title: Valid Post-Selection Inference
Author(s): Kai Zhang* and Richard Berk and Lawrence D. Brown and Andreas Buja and Linda Zhao
Companies: The University of North Carolina at Chapel Hill and University of Pennsylvania and University of Pennsylvania and University of Pennsylvania and University of Pennsylvania
Keywords: Linear regression ; model selection ; multiple comparison ; family-wise error ; high-dimensional inference ; sphere packing
Abstract:

It is common practice in statistical data analysis to perform data-driven variable selection and derive statistical inference from the resulting model. Such inference enjoys none of the guarantees that classical statistical theory provides for tests and confidence intervals when the model has been chosen a priori. We propose to produce valid "post-selection inference" by reducing the problem to one of simultaneous inference and hence suitably widening conventional confidence and retention intervals. 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 Scheffé protection. Importantly it does not depend on the truth of the selected submodel, and hence it produces valid inference even in wrong models. We describe the structure of the simultaneous inference problem and give some asymptotic results.


Authors who are presenting talks have a * after their name.

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