论文标题
Cramer-von Mises测试变更点
Cramer-von Mises tests for Change Points
论文作者
论文摘要
我们研究了两个非参数检验的假设，即一系列独立观察的序列相对于在单个变化点分布变化的替代方案相同分布。这些测试基于在每个可能的变更点计算的Cramer-von Mises两样本测试。一个测试在所有可能的变更点上使用了最大的此类测试统计量。其他所有可能更改点上的平均值。证明平均统计量的大型样本理论可提供有用的p值比引导比引导更快，尤其是在长序列中。分析功率的连续替代方案。对于此类替代序列，平均统计量的限制能力大于其水平。有证据表明，对于最大统计数据，这是不正确的。渐近方法和自举用于构建测试分布。通过蒙特卡洛电力研究检查测试的性能，以进行各种替代分布。
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 Cramer-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.
