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Bootstrap confidence setsunder modelmisspecification

By Vladimir Spokoiny and Mayya Zhilova


A multiplier bootstrap procedure for construction of likelihood-based congidence sets is considered for ginite 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

Topics: likelihood-based bootstrap confidence set, misspecified model, finite sample size, multiplier bootstrap, weighted bootstrap, Gaussian approximation, Pinsker's inequality, 310 Statistik, 330 Wirtschaft, ddc:310, ddc:330
Publisher: Humboldt-Universität zu Berlin, Wirtschaftswissenschaftliche Fakultät
Year: 2014
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