Estimation of a Common Mean and Weighted Means Statistics
共同均值估计与加权均值统计量AI 解读 ↓
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共同均值估计与加权均值统计量
- 研究问题
- 面对实验室间变异、实验室内方差差异及测量次数不等，如何估计共同均值，并为汇总估计给出合理的不确定性？
- 方法与思路
- 作者将 Mandel–Paule 估计解释为简化的极大似然方法，研究实验室数量增大时一类加权均值统计量的分布行为。
- 材料陈述的贡献
- 摘要称研究给出 Mandel–Paule 均值估计的方差估计和近似置信区间，并指出其实验室间方差估计在该设定下不一致。
- 阅读关注点
- 应核对实验室数量增长的渐近设定、组内方差的处理方式、不一致结论的条件，以及均方误差比较限定的方差分布。
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- 依据 OpenAlex 索引摘要，稿件版本未注明；具体渐近条件与比较数值未提供，不能把特定设定的结论推广到所有多组数据。
原文摘要
Measurements made by several laboratories may exhibit nonnegligible between-laboratory variability, as well as different within-laboratory variances. Also, the number of measurements made at each laboratory often differ. Questions of fundamental importance in the analysis of such data are how to form a best consensus mean, and what uncertainty to attach to this estimate. An estimation equation approach due to Mandel and Paule is often used at the National Institute of Standards and Technology (NIST), particularly when certifying standard reference materials. Primary goals of this article are to study the theoretical properties of this method, and to compare it with some alternative methods, in particular to the maximum likelihood estimator (MLE). Toward this end, we show that the Mandel-Paule solution can be interpreted as a simplified version of the maximum likelihood method. A class of weighted means statistics is investigated for situations where the number of laboratories is large. This class includes a modified MLE and the Mandel-Paule procedure. Large-sample behavior of the distribution of these estimators is investigated. This study leads to a utilizable estimate of the variance of the Mandel-Paule statistic and to an approximate confidence interval for the common mean. It is shown that the Mandel-Paule estimator of the between-laboratory variance is inconsistent in this setting. The results of numerical comparison of mean squared errors of these estimators for a special distribution of within-laboratory variances are also reported.