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首页> 外文期刊>Journal of nonparametric statistics >Consistency of choice in nonparametric multiple comparisons
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Consistency of choice in nonparametric multiple comparisons

机译：非参数多重比较中选择的一致性

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摘要

In this paper, we are interested in the inconsistencies that can arise in the context of rank-based multiple comparisons. It is well known that these inconsistencies exist, but we prove that every possible distribution-free rank-based multiple comparison procedure with certain reasonable properties is susceptible to these phenomena. The proof is based on a generalisation of Arrow's theorem, a fundamental result in social choice theory which states that when faced with three or more alternatives, it is impossible to rationally aggregate preference rankings subject to certain desirable properties. Applying this theorem to treatment rankings, we generalise a number of existing results in the literature and demonstrate that procedures that use rank sums cannot be improved. Finally, we show that the best possible procedures are based on the Friedman rank statistic and the it-sample sign statistic, in that these statistics minimise the potential for paradoxical results.
机译：在本文中，我们对在基于等级的多重比较的情况下可能出现的不一致感兴趣。众所周知，存在这些不一致之处，但是我们证明，具有某些合理属性的每种可能的基于无分布的基于秩的多重比较程序都容易受到这些现象的影响。该证明基于阿罗定理的推广，阿罗定理是社会选择理论的基本结果，该理论指出，当面对三个或更多选择时，不可能合理地汇总受某些期望属性约束的偏好排名。将该定理应用于治疗等级，我们在文献中概括了许多现有结果，并证明使用等级总和的程序无法得到改善。最后，我们表明最佳的程序是基于弗里德曼秩统计和it-sample符号统计，因为这些统计使产生悖论结果的可能性降到最低。

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