Inference for change points in high-dimensional data via selfnormalization

Optimal Change-point Testing for High-dimensional Linear Models with Temporal Dependence

“…Change-point testing is a classical problem in statistics and has been extensively studied in the low-dimensional setting, we refer the readers to Aue et al (2009), Shao and Zhang (2010), Matteson and James (2014), Kirch et al (2015) and Zhang and Lavitas (2018) (among many others) for some recent work and Perron (2006) and Aue and Horváth (2013) for comprehensive reviews. More recently, there is a surge of interest in change-point testing under the high-dimensional setting, see for example Horvath and Hušková (2012), Cho and Fryzlewicz (2015), Jirak (2015), Wang and Samworth (2018), Enikeeva and Harchaoui (2019), Wang et al (2021c) and Chakraborty and Zhang (2021). However, these works mainly focus on testing the stability of mean vector or covariance matrices of high-dimensional times series, and we are not aware of any valid change-point testing procedure for high-dimensional linear models.…”

Computationally efficient and data-adaptive changepoint inference in high dimension

“…Among them, Bai (2010), Horváth and Hušková (2012) and Jin et al (2016) considered L 2 -aggregations followed by the maximum operator, i.e., max k=1,...,n−1 p j=1 C 2 0,j (k). A strategy that replaces each C 2 0,j (k) by a self-normalized U-statistic was suggested in Wang et al (2021). With proper normalization, such max-L 2 -type statistic converges to the supremum of some function of a Gaussian process under necessary conditions if H 0 holds, for which the corresponding quantile is usually obtained via simulations.…”

Robust Inference for Change Points in High Dimension

“…High-dimensional data analysis often encounters testing and estimation of change-points in the mean, and it has attracted a lot of attention in statistics recently. See Horváth and Hušková (2012), Jirak (2015), Cho (2016), Wang and Samworth (2018), Liu et al (2020), Wang et al (2022), Zhang et al (2021) and Chen (2021, 2022) for some recent literature. Among the proposed tests and estimation methods, most of them require quite strong moment conditions (e.g., Gaussian or sub-Gaussian assumption, or sixth moment assumption) and some of them also require weak component-wise dependence assumption.…”

“…In particular, our test targets the dense alternative, is robust to heavy-tailedness, and can accommodate both weak and strong coordinate-wise dependence. Our test is built on two recent advances in high-dimensional testing: spatial sign based two sample test developed in Chakraborty and Chaudhuri (2017) and U-statistics based change-point test developed in Wang et al (2022). Spatial sign based tests have been studied in the literature of multivariate data and they are usually used to handle heavy-tailedness, see Oja (2010) for a book-length review.…”

“…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.…”