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February 2020 Uniformly valid confidence intervals post-model-selection
François Bachoc, David Preinerstorfer, Lukas Steinberger
Ann. Statist. 48(1): 440-463 (February 2020). DOI: 10.1214/19-AOS1815

Abstract

We suggest general methods to construct asymptotically uniformly valid confidence intervals post-model-selection. The constructions are based on principles recently proposed by Berk et al. (Ann. Statist. 41 (2013) 802–837). In particular, the candidate models used can be misspecified, the target of inference is model-specific, and coverage is guaranteed for any data-driven model selection procedure. After developing a general theory, we apply our methods to practically important situations where the candidate set of models, from which a working model is selected, consists of fixed design homoskedastic or heteroskedastic linear models, or of binary regression models with general link functions. In an extensive simulation study, we find that the proposed confidence intervals perform remarkably well, even when compared to existing methods that are tailored only for specific model selection procedures.

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François Bachoc. David Preinerstorfer. Lukas Steinberger. "Uniformly valid confidence intervals post-model-selection." Ann. Statist. 48 (1) 440 - 463, February 2020. https://doi.org/10.1214/19-AOS1815

Information

Received: 1 September 2017; Revised: 1 November 2018; Published: February 2020
First available in Project Euclid: 17 February 2020

zbMATH: 07196546
MathSciNet: MR4065169
Digital Object Identifier: 10.1214/19-AOS1815

Subjects:
Primary: 62F12 , 62F25
Secondary: 62F35 , 62J02

Keywords: Inference post-model-selection , regression , uniform asymptotic inference

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.48 • No. 1 • February 2020
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