Abstract

The jackknife is a reliable tool for reducing the bias of a wide range of estimators. This note demonstrates that even such versatile tools have regularity conditions that can be violated even in relatively simple cases, and that caution needs to be exercised in their use. In particular, we show that the jackknife does not provide the expected reliability for bias-reduction for the sample median, because of subtle changes in behavior of the sample median as one moves between even and odd sample sizes. These considerations arose out of class discussions in a MS-level nonparametrics course.

中文翻译：

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应用折刀对样本中位数的影响

摘要

折刀是一种可靠的工具，可以减少各种估计量的偏差。该注释表明，即使是这样的通用工具也具有即使在相对简单的情况下也可能违反的规律性条件，因此在使用它们时需要谨慎。特别是，我们表明折叠刀没有为样本中值减少偏差提供预期的可靠性，因为当样本在偶数和奇数样本大小之间移动时样本中值的行为发生了微妙的变化。这些考虑来自 MS 级非参数课程的课堂讨论。