Valid confidence intervals for post-model-selection predictors
François Bachoc, Hannes Leeb, Benedikt M. Pötscher
The Annals of Statistics · 2019 · Volume 47 · Issue 3
Abstract
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.
Keywords
62F25, 62J05, confidence intervals, Inference post-model-selection, Linear regression, nonstandard targets, optimal post-model-selection predictors
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