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Spokoiny, Vladimir
Zhilova, Mayya
Year of Publication: 
Series/Report no.: 
SFB 649 Discussion Paper 2014-067
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 consistency 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 consistency continues to apply even if the underlying parametric model is misspecified under the so called Small Modeling 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 modeling bias. We illustrate the results with numerical examples for misspecified constant and logistic regressions.
likelihood-based bootstrap con dence set
misspecified model
finite sample size
multiplier bootstrap
weighted bootstrap
Gaussian approximation
Pinsker's inequality
Document Type: 
Working Paper

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