VALID CONFIDENCE INTERVALS FOR POST-MODEL-SELECTION PREDICTORS

• 成果类型: Article
• 署名作者: Bachoc, Francois; Leeb, Hannes; Potscher, Benedikt M.
• 署名单位: Universite de Toulouse; Universite Toulouse III - Paul Sabatier; University of Vienna
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/18-AOS1721
• 发表日期: 2019
• 页码: 1475-1504
• 关键词: VARIABLE SELECTION; inference; estimators; likelihood

摘要

We consider inference post-model-selection in linear regression. In this setting, Berk et al. [Ann. Statist. 41 (2013a) 802-837] recently introduced a class of confidence sets, the so-called PoSI intervals, that cover a certain nonstandard quantity of interest with a user-specified minimal coverage probability, irrespective of the model selection procedure that is being used. In this paper, we generalize the PoSI intervals to confidence intervals for post-model-selection predictors.