@article{Alnssyan2026, 
author = {Badr S. Alnssyan and Abdelaziz Alsubie and Javid Gani Dar},
title = {Robust statistical inference for high-dimensional mean structural breaks under    β-mixing dependence},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {5},
pages = {13149-13173},
keywords = {robust change-point inference, high-dimensional mean shifts, heavy-tailed dependence, β-mixing processes, statistical model, blockwise self-normalization, nonasymptotic testing, finite-sample confidence regions, simulation},
url = {https://www.sciopen.com/article/10.3934/math.2026542},
doi = {10.3934/math.2026542},
abstract = {We studied nonasymptotic inference for a single change-point in the mean of a high-dimensional time series under heavy-tailed marginals and temporal dependence. We developed a robust coordinatewise truncated cumulative sum (CUSUM) process on a trimmed candidate set and paired it with block self-normalization to adapt to an unknown long-run scale. Under    β-mixing dependence and finite    (  2  +  δ  ) moments, we derived explicit deviation bounds for the robust CUSUM process uniformly over candidate split points and coordinates. These bounds yield a finite-sample level-   α test for the existence of a mean change, a finite-sample power guarantee under a separated alternative, and a localization guarantee for the argmax estimator with explicit dependence on    log  ⁡  p, the moment index, and the mixing profile. We also constructed a nonasymptotic confidence set for the change-point location by inverting a localized robust contrast, and we proved a finite-sample diameter bound for the resulting set. The proofs were explicit and included truncation bias control, block coupling under absolute regularity, and bounded-increment Bernstein arguments. A reproducible Monte Carlo study under heavy-tailed AR(1) dependence corroborated the finite-sample size control, power trends, localization behavior, and implementation trade-offs.}
}