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December 2015 Bootstrap confidence sets under model misspecification
Vladimir Spokoiny, Mayya Zhilova
Ann. Statist. 43(6): 2653-2675 (December 2015). DOI: 10.1214/15-AOS1355

Abstract

A multiplier bootstrap procedure for construction of likelihood-based confidence sets is considered for finite samples and a possible model misspecification. Theoretical results justify the bootstrap validity for a small or moderate sample size and allow to control the impact of the parameter dimension $p$: the bootstrap approximation works if $p^{3}/n$ is small. The main result about bootstrap validity continues to apply even if the underlying parametric model is misspecified under the so-called small modelling bias condition. In the case when the true model deviates significantly from the considered parametric family, the bootstrap procedure is still applicable but it becomes a bit conservative: the size of the constructed confidence sets is increased by the modelling bias. We illustrate the results with numerical examples for misspecified linear and logistic regressions.

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Vladimir Spokoiny. Mayya Zhilova. "Bootstrap confidence sets under model misspecification." Ann. Statist. 43 (6) 2653 - 2675, December 2015. https://doi.org/10.1214/15-AOS1355

Information

Received: 1 November 2014; Revised: 1 June 2015; Published: December 2015
First available in Project Euclid: 7 October 2015

zbMATH: 1327.62179
MathSciNet: MR3405607
Digital Object Identifier: 10.1214/15-AOS1355

Subjects:
Primary: 62F25 , 62F40
Secondary: 62E17

Keywords: finite sample size , Gaussian approximation , Likelihood-based bootstrap confidence set , multiplier/weighted bootstrap , Pinsker’s inequality

Rights: Copyright © 2015 Institute of Mathematical Statistics

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Vol.43 • No. 6 • December 2015
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