Jacknife estimation of functions of stratum means
层均值函数的 Jackknife 估计AI 解读 ↓
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层均值函数的 Jackknife 估计
- 研究问题
- 对有限多变量总体的分层样本，如何降低样本均值非线性函数估计量的偏差，并改善相应方差估计的稳定性？
- 方法与思路
- 作者采用逐次删除一个抽样单位的 Jackknife，将全样本与删减样本估计线性组合，并解析推导偏差与样本量关系。
- 材料陈述的贡献
- 摘要称推导推进到二阶 Jackknife 参数和方差估计，处理展开中涉及三阶矩的偏差，并说明单层时与既有方法的渐近联系。
- 阅读关注点
- 应核对逐单位删除时各层权重和抽样设计的处理、矩展开条件，以及一阶与二阶修正及方差稳定性结论。
- 阅读边界
- 依据稿件版本未注明的 OpenAlex 索引摘要；具体估计式与余项条件未给出，不能把矩展开中的偏差消除理解为完全无偏。
原文摘要
SUMMARY The jackknife method of investigating and reducing the bias in nonlinear estimates of parameters is applied to stratified samples from a multivariate population of finite size. Attention is focused on estimators that can be expressed as functions of sample means. As in other applications of the jackknife method, an approximate relationship between the bias in an estimator and the sample size is exploited to reduce this bias by employing a linear combination of an estimate computed from all the data and several estimates each computed after omitting part of the data. Unlike some other applications to stratified sampling, however, where the data omitted are those for a group of sampling units that cut across all strata, the present application involves omitting just one sampling unit at a time, thereby compacting the region where approximate relationships are assumed to hold, and increasing the stability of the variance estimates. The relationships are derived by an analytic approach. Results are carried out far enough for use in second-order jackknife estimates of parameters and variances so as to eliminate bias to third-order moments of the variables observed. When there is just one stratum, the first-order estimators defined by equations (4.3) and (6-1), which are unbiased to second-order moments, are asymptotically the same -as those proposed by Tukey (1958).