VALID POST-SELECTION INFERENCE

• 成果类型: Article
• 署名作者: Berk, Richard; Brown, Lawrence; Buja, Andreas; Zhang, Kai; Zhao, Linda
• 署名单位: University of Pennsylvania
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/12-AOS1077
• 发表日期: 2013
• 页码: 802-837
• 关键词: MAXIMUM-LIKELIHOOD ESTIMATORS; model-selection; confidence-intervals; gaussian regression; conditional level; PROPERTY; students; Lasso

摘要

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 Scheffe 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.