Convergence of U-Processes in H\"older Spaces with Application to Robust Detection of a Changed Segment

TL;DR

This paper introduces a robust change detection method for time series using Wilcoxon-based statistics, supported by theoretical limit theorems and demonstrated through simulations and real data application.

Contribution

It develops a new robust test statistic for epidemic change detection based on U-processes in H"older spaces, with proven asymptotic properties.

Findings

The Wilcoxon-based test performs well with heavy-tailed data.

Functional limit theorems for U-processes are established.

Simulation studies confirm the effectiveness of the proposed method.

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.