Robust inference for change points in high dimension

Feiyu Jiang, Runmin Wang, Xiaofeng Shao

Research output: Contribution to journalArticlepeer-review


This paper proposes a new test for a change point in the mean of high-dimensional data based on the spatial sign and self-normalization. The test is easy to implement with no tuning parameters, robust to heavy-tailedness and theoretically justified with both fixed-n and sequential asymptotics under both null and alternatives, where n is the sample size. We demonstrate that the fixed-n asymptotics provide a better approximation to the finite sample distribution and thus should be preferred in both testing and testing-based estimation. To estimate the number and locations when multiple change-points are present, we propose to combine the p-value under the fixed-n asymptotics with the seeded binary segmentation (SBS) algorithm. Through numerical experiments, we show that the spatial sign based procedures are robust with respect to the heavy-tailedness and strong coordinate-wise dependence, whereas their non-robust counterparts proposed in Wang et al. (2022)[28] appear to under-perform. A real data example is also provided to illustrate the robustness and broad applicability of the proposed test and its corresponding estimation algorithm.

Original languageEnglish (US)
Article number105114
JournalJournal of Multivariate Analysis
StatePublished - Jan 2023


  • Change points
  • High dimensional data
  • Segmentation
  • Self-normalization
  • Spatial sign

ASJC Scopus subject areas

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty


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