A robust bootstrap change point test for high-dimensional location parameter

We consider the problem of change point detection for high-dimensional distributions in a location family when dimension can be much larger than sample size. In analysis, widely used cumulative sum (CUSUM) statistics are sensitive to outliers and heavy-tailed distributions. this paper, we propose robust, tuning-free (i.e., fully data-dependent), easy-to-implement test that enjoys strong theoretical guarantees. To achieve robust purpose nonparametric setting, formulate multivariate U-statistics framework with anti-symmetric nonlinear kernels. Specifically, within-sample noise is canceled out by anti-symmetry kernel, while signal distortion under certain kernels controlled such between-sample magnitude preserving. A (half) jackknife multiplier bootstrap (JMB) tailored setting proposed calibrate distribution our ??-norm aggregated statistic. Subject mild moment conditions on kernels, derive uniform rates convergence JMB approximate sampling statistic, analyze its size power properties. Extensions multiple testing estimation discussed illustration from numerical studies.