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A test of concordance based on Gini's mean difference

机译：基于基尼均值差的一致性检验

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摘要

A new rank correlation index, which can be used to measure the extent of concordance or discordance between two rankings, is proposed. This index is based on Gini's mean difference computed on the totals ranks corresponding to each unit and it turns out to be a special case of a more general measure of the agreement of m rankings. The proposed index can be used in a test for the independence of two criteria used to rank the units of a sample, against their concordance/discordance. It can then be regarded as a competitor of other classical methods, such as Kendall's tau. The exact distribution of the proposed test-statistic under the null hypothesis of independence is studied and its expectation and variance are determined; moreover, the asymptotic distribution of the test-statistic is derived. Finally, the implementation of the proposed test and its performance are discussed.
机译：提出了一种新的等级相关指数，可以用来衡量两个等级之间的一致性或不一致程度。该指数基于基尼的平均差，该平均差是根据与每个单元相对应的总排名计算得出的，事实证明这是对m个排名的一致性进行更一般性度量的特例。建议的索引可用于测试两个标准的独立性，这两个标准用于对样本单位进行一致性/不一致评估。然后可以将其视为其他经典方法（例如Kendall's tau）的竞争对手。研究了在独立性为零的假设下所提出的检验统计量的精确分布，并确定了其期望值和方差；此外，推导了检验统计量的渐近分布。最后，讨论了所提出的测试的实现及其性能。

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