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

Mengjia Yu, Xiaohui Chen

Research output: Contribution to journalArticlepeer-review


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

Original languageEnglish (US)
Pages (from-to)1096-1152
Number of pages57
JournalElectronic Journal of Statistics
Issue number1
StatePublished - 2022


  • Bootstrap
  • Gaussian ap-proximation
  • U-statistics
  • change point analysis
  • high-dimensional data

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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