Convergence of U-Processes in Hölder Spaces with Application to Robust Detection of a Changed Segment

Abstract: 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 H\"older spaces. We also study the finite sample behavior via simulations and apply the statistic to a real data example.