Robust Inference for Change Points in High Dimension

TL;DR

This paper introduces a robust, tuning-free test for detecting change points in high-dimensional data using spatial signs and self-normalization, with theoretical justification and practical effectiveness demonstrated through simulations and real data.

Contribution

It develops a new change point detection method based on spatial signs that is robust to heavy tails and dependence, with fixed-$n$ asymptotics providing better finite-sample approximation.

Findings

The proposed test is robust to heavy-tailed distributions.

The fixed-$n$ asymptotics outperform traditional approaches.

The method effectively detects multiple change points in high-dimensional data.

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) 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.