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BOOTSTRAP CONFIDENCE SETS UNDER MODEL MISSPECIFICATION
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DOI：10.1214/15-AOS1355.png)
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摘要
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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.
Keyword:
Likelihood-based bootstrap confidence set
finite sample size
multiplier/weighted bootstrap
Gaussian approximation
Pinsker's inequality
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