To detect a changed segment (so called epedimic changes) in a time series, variants of the CUSUM statistic are frequently used. However, they are sensitive to outliers in the data and do not perform well for heavy tailed data, especially when short segments get a high weight in the test statistic. We will present a robust test statistic for epidemic changes based on the Wilcoxon statstic. To study their asymptotic behavior, we prove functional limit theorems for U-processes in Holder spaces. We also study the finite sample behavior via simulations and apply the statistics to a real data example.

中文翻译：

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Hölder 空间中 U 过程的收敛，并应用于对变化段的稳健检测

为了检测时间序列中的变化段（所谓的流行病变化），经常使用 CUSUM 统计量的变体。然而，它们对数据中的异常值很敏感，对于重尾数据表现不佳，尤其是当短段在测试统计中获得高权重时。我们将提供基于 Wilcoxon 统计量的流行变化的稳健检验统计量。为了研究它们的渐近行为，我们证明了 Holder 空间中 U 过程的泛函极限定理。我们还通过模拟研究有限样本行为，并将统计数据应用于真实数据示例。