Bootstrap confidence sets under model misspecification

Vladimir Spokoiny, Mayya Zhilova

Research output: Contribution to journalArticlepeer-review

24 Citations (Scopus)

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 p3/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.

Original languageEnglish
Pages (from-to)2653-2675
Number of pages23
JournalAnnals of Statistics
Volume43
Issue number6
DOIs
Publication statusPublished - Dec 2015
Externally publishedYes

Keywords

  • Finite sample size
  • Gaussian approximation
  • Likelihood-based bootstrap confidence set
  • Multiplier/ weighted bootstrap
  • Pinsker's inequality

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