ON THE CHOICE OF m IN THE m OUT OF n BOOTSTRAP AND CONFIDENCE BOUNDS FOR EXTREMA
ON THE CHOICE OF m IN THE m OUT OF n BOOTSTRAP AND CONFIDENCE BOUNDS FOR EXTREMA
复制标题
论m out of n bootstrap中m的选择和极值的置信界
DOI：
--
复制
发表时间：
2008
期刊：
影响因子：
--
通讯作者：
A. Sakov
中科院分区：
文献类型：
--
作者：
P. Bickel;A. Sakov
用来确认身份。对于大小为n的样本，普通的Bootstrap(Efron(1979))在许多情况下是一致的，但在重要的例子中它可能失败(Bickel，Gotze和van Zwet(1997))。使用大小为m的引导样本(其中m！1和m/n！0)通常可以解决问题(Bickel等人。(1997年)、《波利蒂斯和罗马诺》(1994年))。M的选择是一个关键问题。本文考虑了Bickel，Gotze和van Zwet(Personal Communication)提出的一种选择m的自适应规则，给出了该规则一阶有效性的一般充分条件，并考虑了它在普通引导失效和正常工作时的高阶行为。然后，我们在设置高百分位数的置信限(例如渐近预期最大值)的背景下检查该规则的行为。
For i.i.d. samples of size n, the ordinary bootstrap (Efron (1979)) is known to be consistent in many situations, but it may fail in important examples (Bickel, Gotze and van Zwet (1997)). Using bootstrap samples of size m, where m ! 1 and m/n ! 0, typically resolves the problem (Bickel et al. (1997), Politis and Romano (1994)). The choice of m is a key issue. In this paper, we consider an adaptive rule, proposed by Bickel, Gotze, and van Zwet (personal communication), to pick m. We give general sufficient conditions for first order validity ofthe rule, and consider its higher order behavior when the ordinary bootstrap fails, and when it works. We then examine the behavior of the rule in the context of setting confidence bounds on high percentiles, such as the asymptotic expected maximum.