Robust statistical inference for high-dimensional mean structural breaks under $ \beta $-mixing dependence

Badr S. Alnssyan; Abdelaziz Alsubie; Javid Gani Dar; Badr S. Alnssyan; Abdelaziz Alsubie; Javid Gani Dar

doi:10.3934/math.2026542

AIMS Mathematics

2026, Volume 11, Issue 5: 13149-13173. doi: 10.3934/math.2026542

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Research article

Robust statistical inference for high-dimensional mean structural breaks under $ \beta $-mixing dependence

1.
Department of Management Information Systems, College of Business and Economics, Qassim University, Buraydah 51452, Saudi Arabia
2.
Department of Basic Sciences, College of Science and Theoretical Studies, Saudi Electronic University, Riyadh 11673, Saudi Arabia
3.
Department of Applied Sciences, Symbiosis Institute of Technology, Symbiosis International (Deemed) University, Lavale, Pune 412115, India

Received: 04 March 2026 Revised: 04 April 2026 Accepted: 22 April 2026 Published: 12 May 2026
MSC : Primary 62G32, 62M10, 62H15; Secondary 60G10, 60E15, 62F03

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 $ \beta $-mixing dependence and finite $ (2+\delta) $ 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-$ \alpha $ 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.
- robust change-point inference,
- high-dimensional mean shifts,
- heavy-tailed dependence,
- $ \beta $-mixing processes,
- statistical model,
- blockwise self-normalization,
- nonasymptotic testing,
- finite-sample confidence regions,
- simulation
Citation: Badr S. Alnssyan, Abdelaziz Alsubie, Javid Gani Dar. Robust statistical inference for high-dimensional mean structural breaks under $ \beta $-mixing dependence[J]. AIMS Mathematics, 2026, 11(5): 13149-13173. doi: 10.3934/math.2026542

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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 $ \beta $-mixing dependence and finite $ (2+\delta) $ 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-$ \alpha $ 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.

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