Robust inference for change points in high dimension

Feiyu Jiang, Runmin Wang and Xiaofeng Shao

Journal of Multivariate Analysis, 2023, vol. 193, issue C

Abstract: 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.

Keywords: Change points; High dimensional data; Segmentation; Self-normalization; Spatial sign (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1016/j.jmva.2022.105114

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