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Activity Number: 600
Type: Contributed
Date/Time: Wednesday, August 12, 2015 : 2:00 PM to 3:50 PM
Sponsor: IMS
Abstract #315174
Title: Valid Confidence Intervals for Post-Model-Selection Predictors
Author(s): Francois Bachoc* and Hannes Leeb and Benedikt M. Pötscher
Companies: University of Vienna and University of Vienna and University of Vienna
Keywords: inference post-model-selection ; confidence intervals ; linear regression
Abstract:

We consider inference post-model-selection in linear regression. In this setting, Berk et al. (Annals of Statistics, 2013) recently introduced a class of confidence sets, the so-called PoSI intervals, that cover a certain non-standard quantity of interest with a user-specified minimal coverage probability, irrespective of the model selection procedure that is being used. In this talk, we generalize the PoSI intervals to post-model-selection predictors. We define two non-standard predictors: the first one being the natural extension of the quantity of interest of Berk et al., the second one having more relevant optimality properties. For these two predictors, we construct confidence intervals, extending those of Berk et al., and give corresponding algorithms and exact and asymptotic coverage properties. We reinforce these results by a simulation study.


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