Title: A robust and high-dimensional bootstrap change point test for location parameter
Authors: Mengjia Yu - University of Illinois at Urbana-Champaign (United States) [presenting]
Xiaohui Chen - University of Illinois Urbana-Champaign (United States)
Abstract: In change point analysis, the widely used cumulative sum (CUSUM) statistics are sensitive to outliers. We propose a robust test for change point detection problem of location-shift in high dimensions when the dimension $p$ can be much larger than the sample size $n$. To achieve the robustness purpose in a nonparametric setting, we consider signal cancellations in the general U-statistics framework with anti-symmetric kernels of order 2. To calibrate the distribution of our test statistic, a Gaussian multiplier bootstrap is proposed. Subject to mild conditions on kernels, we derive the uniform rates of convergence of the multiplier bootstrap to the sampling distribution of the test statistic. The proposed test is fully data-dependent without any tuning parameter, and numeric studies are provided.