ON THE UNIFORM ASYMPTOTIC VALIDITY OF SUBSAMPLING AND THE BOOTSTRAP

• 成果类型: Article
• 署名作者: Romano, Joseph P.; Shaikh, Azeem M.
• 署名单位: Stanford University; Stanford University; University of Chicago
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/12-AOS1051
• 发表日期: 2012
• 页码: 2798-2822
• 关键词: IDENTIFIED ECONOMETRIC-MODELS; moment inequalities; inference; parameters; selection; estimators; RISK; set

摘要

This paper provides conditions under which subsampling and the bootstrap can be used to construct estimators of the quantiles of the distribution of a root that behave well uniformly over a large class of distributions P. These results are then applied (i) to construct confidence regions that behave well uniformly over P in the sense that the coverage probability tends to at least the nominal level uniformly over P and (ii) to construct tests that behave well uniformly over P in the sense that the size tends to no greater than the nominal level uniformly over P. Without these stronger notions of convergence, the asymptotic approximations to the coverage probability or size may be poor, even in very large samples. Specific applications include the multivariate mean, testing moment inequalities, multiple testing, the empirical process and U-statistics.