论文标题
通过部分排序进行非参数测试
Nonparametric testing via partial sorting
论文作者
论文摘要
在本文中，我们介绍了部分分类数据以设计非参数测试的想法。这种方法引起了对数据的顺序和基础分布敏感的测试。我们特别关注的是使用气泡排序算法部分对数据进行分类的测试。我们表明，数据的功能（称为经验气泡排序曲线）均匀收敛到限制曲线。我们根据经验曲线及其极限之间的距离定义了合适的测试。测试统计数据的渐近分布是Kolmogorov分布的概括。我们在几个示例中应用测试，并观察到它的表现优于经典的非参数测试，以适当选择的排序水平。
In this paper we introduce the idea of partially sorting data to design nonparametric tests. This approach gives rise to tests that are sensitive to both the order and the underlying distribution of the data. We focus in particular on a test that uses the bubble sort algorithm to partially sort the data. We show that a function of the data, referred to as the empirical bubble sort curve, converges uniformly to a limiting curve. We define a goodness-of-fit test based on the distance between the empirical curve and its limit. The asymptotic distribution of the test statistic is a generalization of the Kolmogorov distribution. We apply the test in several examples and observe that it outperforms classical nonparametric tests for appropriately chosen sorting levels.
