U-过程在Hölder空间中的收敛性及其在变段鲁棒检测中的应用
Convergence of U-Processes in Hölder Spaces with Application to Robust Detection of a Changed Segment
摘要：
为了检测时间序列中的变化段（所谓的流行变化），经常使用MANUUM统计量的变体。然而，它们对数据中的离群值敏感，并且对于重尾数据表现不佳，特别是当短片段在检验统计量中获得高权重时。我们将基于Wilcoxon统计量为流行病变化提供一个稳健的检验统计量。为了研究U-过程的渐近性态，我们证明了U-过程在Hölder空间中的泛函极限定理.我们还研究了有限样本的行为，通过模拟和应用统计的真实数据的例子。
英文摘要：
To detect a changed segment (so called epidemic 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 statistic. To study their asymptotic behavior, we prove functional limit theorems for U-processes in Hölder spaces. We also study the finite sample behavior via simulations and apply the statistic to a real data example.
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