Bootstrap confidence sets under model misspecification

Vladimir Spokoiny and Mayya Zhilova

No 2014-067, SFB 649 Discussion Papers from Humboldt University Berlin, Collaborative Research Center 649: Economic Risk

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 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.

Keywords: likelihood-based bootstrap con dence set; misspecified model; finite sample size; multiplier bootstrap; weighted bootstrap; Gaussian approximation; Pinsker's inequality (search for similar items in EconPapers)
JEL-codes: C13 C15 (search for similar items in EconPapers)
Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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