AI 中文总结
本文提出尖锐逐路径信噪比阈值，证明带岭正则化的准最大似然断点估计在对比度超过波动时一致，并推广至普适因子模型。
AI 中文摘要
我们为多元时间序列二阶矩结构中主导断点的准最大似然（QML）估计建立了尖锐的逐路径信噪比准则：当区间间对比度超过区间内波动一个显式因子时，QML估计量是一致的，而低于该阈值时全局恢复可能失败。该结果由两项创新驱动。首先，该框架是逐路径的：不对数据施加随机模型。其次，对数行列式目标函数带有加性岭正则化：它消除了端点边界层，因此无需对候选集进行修剪，并且调整岭参数可弱化一致性条件。作为主定理的一个应用，我们建立了在维度随样本量发散的普适因子模型中QML断点估计的一致性，适用于完全一般的误差项——不一定是独立的、特异性的，甚至不一定是随机的。
英文摘要
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.
Comments47 pages, 5 figures. Ancillary files: Python scripts generating Figures 1-4
