In this paper, we consider some statistical measures of deviation from the perfect ranking in the framework of ranked set sampling. We use nonparametric approach for testing the null hypothesis for perfect ranking. The distance-based Mallows’ models with appropriate distance on permutations are suggested in the case of imperfect ranking. Some asymptotic results for the corresponding error probability matrix are derived for the models based on Spearman’s footrule and Spearman’s rho. We propose an EM algorithm for estimating the unknown parameter in the Mallows’ models in order to compare the power of the presented test statistics.

中文翻译：

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Mallows的排名集采样中排名不完美的模型

在本文中，我们考虑了在排名集抽样框架内偏离完美排名的一些统计度量。我们使用非参数方法来检验零假设，以获得完美排名。在排名不完善的情况下，建议使用基于距离的Mallows模型（在排列上具有适当的距离）。基于Spearman的法则和Spearman的rho推导了模型相应误差概率矩阵的一些渐近结果。我们提出了一种EM算法来估计Mallows模型中的未知参数，以便比较所提供的测试统计量的功效。