标题： 关于子抽样和引导法的统一渐近有效性 显示英文标题

标题： On the uniform asymptotic validity of subsampling and the bootstrap

摘要： 本文提供了在何种条件下可以使用子抽样和引导法来构造根分布分位数的估计量，这些估计量在一大类分布上表现良好，且在整个分布类中一致地表现良好$\mathbf{P}$。 这些结果随后被应用于（i）构造在$\mathbf{P}$上表现良好的置信区域，即覆盖概率在$\mathbf{P}$上一致地趋于至少名义水平，以及（ii）构造在$\mathbf{P}$上表现良好的检验，即大小在$\mathbf{P}$上一致地趋于不超过名义水平。 如果没有这些更强的收敛概念，即使在非常大的样本中，对覆盖概率或大小的渐近近似也可能很差。 具体应用包括多元均值、检验矩不等式、多重检验、经验过程和U统计量。 显示英文摘要

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 $\mathbf{P}$. These results are then applied (i) to construct confidence regions that behave well uniformly over $\mathbf{P}$ in the sense that the coverage probability tends to at least the nominal level uniformly over $\mathbf{P}$ and (ii) to construct tests that behave well uniformly over $\mathbf{P}$ in the sense that the size tends to no greater than the nominal level uniformly over $\mathbf{P}$. 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.