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May 2015 On Various Confidence Intervals Post-Model-Selection
Hannes Leeb, Benedikt M. Pötscher, Karl Ewald
Statist. Sci. 30(2): 216-227 (May 2015). DOI: 10.1214/14-STS507

Abstract

We compare several confidence intervals after model selection in the setting recently studied by Berk et al. [ Ann. Statist. 41 (2013) 802–837], where the goal is to cover not the true parameter but a certain nonstandard quantity of interest that depends on the selected model. In particular, we compare the PoSI-intervals that are proposed in that reference with the “naive” confidence interval, which is constructed as if the selected model were correct and fixed a priori (thus ignoring the presence of model selection). Overall, we find that the actual coverage probabilities of all these intervals deviate only moderately from the desired nominal coverage probability. This finding is in stark contrast to several papers in the existing literature, where the goal is to cover the true parameter.

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Hannes Leeb. Benedikt M. Pötscher. Karl Ewald. "On Various Confidence Intervals Post-Model-Selection." Statist. Sci. 30 (2) 216 - 227, May 2015. https://doi.org/10.1214/14-STS507

Information

Published: May 2015
First available in Project Euclid: 3 June 2015

zbMATH: 1332.62154
MathSciNet: MR3353104
Digital Object Identifier: 10.1214/14-STS507

Rights: Copyright © 2015 Institute of Mathematical Statistics

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Vol.30 • No. 2 • May 2015
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