BOOTSTRAP CONFIDENCE SETS UNDER MODEL MISSPECIFICATION

• 成果类型: Article
• 署名作者: Spokoiny, Vladimir; Zhilova, Mayya
• 署名单位: Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Humboldt University of Berlin; Moscow Institute of Physics & Technology; Russian Academy of Sciences; HSE University (National Research University Higher School of Economics)
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/15-AOS1355
• 发表日期: 2015
• 页码: 2653-2675
• 关键词: multiplier bootstrap; Wild Bootstrap; jackknife; tests

摘要

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.