The Bayes classification rule offers the optimal classifier, minimizing the classification error rate, whereas the Neyman–Pearson lemma offers the optimal family of classifiers to maximize the detection rate for any given false alarm rate. These motivate studies on comparing classifiers based on similarities between the classifiers and the optimal. In this article, we define partial order relations on classifiers and families of classifiers, based on rankings of rate function values and rankings of test function values, respectively. Each partial order relation provides a sufficient condition, which yields better classification error rates or better performance on the receiver operating characteristic analysis. Various examples and applications of the partial order theorems are discussed to provide comparisons of classifiers and families of classifiers, including the comparison of cross‐validation methods, training data that contains outliers, and labelling errors in training data. The Canadian Journal of Statistics 48: 152–166; 2020 © 2019 Statistical Society of Canada

中文翻译：

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偏序关系用于分类比较

贝叶斯分类规则提供了最佳的分类器，从而最大程度地降低了分类错误率，而内曼-皮尔森引理提供了最佳的分类器族，以在任何给定的误报率下最大化检测率。这些激励了基于分类器和最优值之间的相似性来比较分类器的研究。在本文中，我们分别基于比率函数值的等级和测试函数值的等级定义分类器和分类器族上的偏序关系。每个偏序关系都提供了充分的条件，从而在接收器工作特性分析上产生了更好的分类错误率或更好的性能。加拿大统计杂志48：152–166；加拿大统计局。2020©2019加拿大统计学会