Hubeyb Gurdogan, Georg Menz
arXiv 10 Sep 2026 · Mathematics — Statistics Theory
arXiv:2609.12271 · PDF · Extracted main text
We establish a sharp pathwise signal-to-noise criterion for quasi-maximum-likelihood (QML) estimation of a dominant breakpoint in the second-moment structure of a multivariate time series: the QML estimator is consistent whenever the between-regime contrast exceeds the within-regime fluctuation by an explicit factor, and below this threshold global recovery can fail. Two innovations drive the result. First, the framework is pathwise: no stochastic model is imposed on the data. Second, the log-determinant objective carries an additive ridge regularization: it removes the endpoint boundary layers, so no trimming of the candidate set is required, and tuning the ridge weakens the consistency condition. As an application of the main theorem, we establish consistency of QML breakpoint estimation in pervasive factor models whose dimension diverges with the sample size, for completely general error terms -- not necessarily independent, idiosyncratic, or even random.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | J. Duan, J. Bai, and X. Han (2023) Quasi-maximum likelihood estimation of break point in high-dimensional factor models | 1.000 | 8 | 3 | 100% |
| 2 | J. Bai, X. Han, and Y. Shi (2020) Estimation and inference of change points in high-dimensional factor models | 0.737 | 3 | 2 | 100% |
| 3 | J. Bai (2003) Inferential theory for factor models of large dimensions | 0.644 | 2 | 2 | 100% |
| 4 | M. Basseville and I. V. Nikiforov (1993) Detection of Abrupt Changes: Theory and Application | 0.644 | 2 | 2 | 100% |
| 5 | M. Csörgo and L. Horváth (1997) Limit Theorems in Change-Point Analysis | 0.644 | 2 | 2 | 100% |
| 6 | A. Gretton, K. M. Borgwardt, M. J. Rasch, B. Schölkopf, and A. J. Sm… (2012) A kernel two-sample test | 0.644 | 2 | 2 | 100% |
| 7 | D. S. Matteson and N. A. James (2014) A nonparametric approach for multiple change point analysis of multivariate data | 0.644 | 2 | 2 | 100% |
| 8 | E. S. Page (1954) Continuous inspection schemes | 0.644 | 2 | 2 | 100% |
| 9 | T. Wang and R. J. Samworth (2018) High dimensional change point estimation via sparse projection | 0.644 | 2 | 2 | 100% |
| 10 | C.-S. J. Chu, K. Hornik, and C.-M. Kuan (1995) Mosum tests for parameter constancy | 0.644 | 2 | 2 | 100% |
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