THE NUMERICAL BOOTSTRAP

• 成果类型: Article
• 署名作者: Hong, Han; Li, Jessie
• 署名单位: Stanford University; University of California System; University of California Santa Cruz
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/19-AOS1812
• 发表日期: 2020
• 页码: 397-412
• 关键词: inference; replacement; models

摘要

This paper proposes a numerical bootstrap method that is consistent in many cases where the standard bootstrap is known to fail and where the m-out-of-n bootstrap and subsampling have been the most commonly used inference approaches. We provide asymptotic analysis under both fixed and drifting parameter sequences, and we compare the approximation error of the numerical bootstrap with that of the m-out-of-n bootstrap and subsampling. Finally, we discuss applications of the numerical bootstrap, such as constrained and unconstrained M-estimators converging at both regular and nonstandard rates, Laplace-type estimators, and test statistics for partially identified models.