Abstract Paired comparison data is often used to rank or order a set of items. In this paper we study a method for estimating the parameters associated with completely ordered cardinal paired comparison data. The analysis is carried out within the framework of graphical linear models but rather than using the least squares estimator, which may be difficult to analyze, we consider the average of all tree-based estimators for the connected comparison graph. The resulting estimator is a simple linear function of the sufficient statistics and has an easy to understand graph-theoretic interpretation. The statistical properties of this estimator are studied and it is shown to be unbiased, strongly consistent and asymptotically normal. Examples and numerical comparisons are provided and extensions are discussed.

中文翻译：

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配对比较数据的基于图的估计器

摘要 配对比较数据通常用于对一组项目进行排名或排序。在本文中，我们研究了一种估计与完全有序的基数配对比较数据相关的参数的方法。分析是在图形线性模型的框架内进行的，而不是使用可能难以分析的最小二乘估计量，我们考虑连接比较图的所有基于树的估计量的平均值。所得估计量是充分统计量的简单线性函数，并且具有易于理解的图论解释。研究了该估计量的统计特性，结果表明它是无偏的、强一致的和渐近正态的。提供了示例和数值比较，并讨论了扩展。