Abstract：
Many statistical methods (estimators) are available for estimating the consensus value (or average effect) and heterogeneity variance in interlaboratory studies or meta-analyses. These estimators are all valid because they are developed from or supported by certain statistical principles. However, no estimator can be perfect and must have error or uncertainty (known as estimator uncertainty). For a given dataset, the consensus value and heterogeneity variance given by different estimators can often differ significantly. Consequently, the choice of different estimators can affect the conclusion of an interlaboratory study or meta-analysis. However, there is no universally accepted metric for determining which estimator is optimal among a set of candidate estimators. Instead of selecting and using a single estimator, this paper proposes an estimator-averaging approach to combine a set of individual estimators. The final averaged estimator is a linear combination of individual estimators, which accounts for three sources of uncertainties including the estimator uncertainty. Monte Carlo simulations were performed to examine the long-run performance of four individual estimators and the proposed averaged estimators. A case study: the determination of the Newtonian constant of gravitation is presented, where 10 individual estimators (eight frequentist weighted average methods and two Bayesian methods) are combined using the proposed estimator-averaging approach.
摘要：
许多统计方法（估计器）可用于估计实验室间研究或荟萃分析中的共识值（或平均效应）和异质性方差。这些估计器都是有效的，因为它们是从某些统计原理发展而来的或得到某些统计原理的支持。然而,任何估计器都不可能是完美的，必须有误差或不确定性(称为估计器不确定性)。对于给定的数据集，不同估计量给出的一致性值和异质性方差通常会有显著差异。因此,不同估计量的选择会影响实验室间研究或荟萃分析的结论.然而,在一组候选估计器中，没有普遍接受的度量来确定哪个估计器是最优的。而不是选择和使用单个估计器，本文提出了一种估计平均方法来组合一组个体估计。最终的平均估计器是各个估计器的线性组合，这说明了三个不确定因素的来源，包括估计器的不确定因素。进行了蒙特卡罗模拟，以检查四个单独估计器和建议的平均估计器的长期性能。一个案例研究：给出了牛顿引力常数的确定，其中使用所提出的估计平均方法组合了十个单独的估计器（八个频率加权平均方法和两个贝叶斯方法）。本文受版权保护。保留所有权利。
