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

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.