We study two nonparametric tests of the hypothesis that a sequence of independent observations is identically distributed against the alternative that at a single change point the distribution changes. The tests are based on the Cramér–von Mises two-sample test computed at every possible change point. One test uses the largest such test statistic over all possible change points; the other averages over all possible change points. Large sample theory for the average statistic is shown to provide useful p-values much more quickly than bootstrapping, particularly in long sequences. Power is analyzed for contiguous alternatives. The average statistic is shown to have limiting power larger than its level for such alternative sequences. Evidence is presented that this is not true for the maximal statistic. Asymptotic methods and bootstrapping are used for constructing the test distribution. Performance of the tests is checked with a Monte Carlo power study for various alternative distributions.

中文翻译：

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变化点的 Cramer-von Mises 检验

我们研究了假设的两个非参数检验，即一系列独立观察结果是相同分布的，而另一种情况是在单个变化点分布发生变化。这些测试基于在每个可能的变化点计算的 Cramér-von Mises 两样本测试。一项测试在所有可能的变化点上使用最大的此类测试统计量；所有可能变化点的其他平均值。显示平均统计量的大样本理论可提供有用的p-值比引导快得多，特别是在长序列中。对连续备选方案的功率进行分析。显示平均统计量的限制功率大于此类替代序列的水平。有证据表明这对于最大统计量是不正确的。渐近方法和自举用于构建测试分布。使用 Monte Carlo 功效研究检查各种替代分布的测试性能。