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.
Original language | English (US) |
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Article number | 105114 |
Journal | Journal of Multivariate Analysis |
Volume | 193 |
DOIs | |
State | Published - Jan 2023 |
Keywords
- Change points
- High dimensional data
- Segmentation
- Self-normalization
- Spatial sign
ASJC Scopus subject areas
- Statistics and Probability
- Numerical Analysis
- Statistics, Probability and Uncertainty