Estimation of a common mean and weighted means statistics
Estimation of a common mean and weighted means statistics
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DOI：
10.2307/2669626
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发表时间：
1998-03-01
影响因子：
3.7
通讯作者：
Vangel, MG
中科院分区：
文献类型：
--
作者：
Rukhin, AL;Vangel, MG
由几个实验室进行的测量可能会显示出不可忽略的实验室间变异性，以及不同的实验室内方差。此外，在每个实验室进行的测量次数往往不同。在分析这些数据时，最重要的问题是如何形成一个最佳的共识平均值，以及这种估计的不确定性。Mandel和Paule提出的估算方程法经常被美国国家标准与技术研究院（NIST）使用，特别是在认证标准参考物质时。本文的主要目标是研究这种方法的理论性质，并将其与一些替代方法进行比较，特别是最大李克森估计（MLE）。为此，我们表明，Mandel-Paule解决方案可以解释为一个简化版本的最大似然法。针对实验室数量较多的情况，研究了一类加权平均统计量。这个类包括修改的MLE和Mandel-Paule程序。这些估计的分布的大样本行为进行了研究。这项研究导致一个有用的估计Mandel-Paule统计量的方差和近似置信区间的共同均值。结果表明，在这种情况下，实验室间方差的Mandel-Paule估计量不一致。还报告了实验室内方差特殊分布的这些估计量的均方误差的数值比较结果。
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.