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.

翻译：在本文中,我们引入了对数据进行部分分类以设计非参数测试的想法。 这种方法产生了对数据顺序和基本分布都敏感的测试。 我们特别侧重于使用气泡分类算法对数据进行部分分类的测试。 我们显示,被称为实验性气泡分类曲线的数据函数与限制曲线一致。 我们根据实验性曲线与其极限之间的距离定义了一种良好的测试标准。 测试统计数据的无症状分布是科多洛夫分布的概括性。 我们在若干例子中应用了测试,并观察到它比典型的非参数测试更符合适当选择的排序水平。