论文标题
超出渐近正态性的经验引导法的渐近学
Asymptotics of the Empirical Bootstrap Method Beyond Asymptotic Normality
论文作者
论文摘要
用于统计推断的最常用方法之一是经验引导程序，当估计器的限制分布未知时，这尤其是权宜的。然而，尽管其无处不在，但其理论特性对于非杂质正常估计器仍未得到很好的理解。在本文中，在稳定条件下，我们建立了经验自举估计器的限制分布，从而导致其渐近一致的严格条件，并量化收敛速度。此外，我们提出了三种替代方法来使用Bootstrap方法来构建置信区间，并提供保证。最后，我们通过一系列示例来说明结果的普遍性和紧密性，包括统一的置信频带，两样本内核测试，Minmax随机程序以及堆叠估算器的经验风险。
One of the most commonly used methods for forming confidence intervals for statistical inference is the empirical bootstrap, which is especially expedient when the limiting distribution of the estimator is unknown. However, despite its ubiquitous role, its theoretical properties are still not well understood for non-asymptotically normal estimators. In this paper, under stability conditions, we establish the limiting distribution of the empirical bootstrap estimator, derive tight conditions for it to be asymptotically consistent, and quantify the speed of convergence. Moreover, we propose three alternative ways to use the bootstrap method to build confidence intervals with coverage guarantees. Finally, we illustrate the generality and tightness of our results by a series of examples, including uniform confidence bands, two-sample kernel tests, minmax stochastic programs and the empirical risk of stacked estimators.
