论文标题
在时间依赖性下，高维回归模型中的更改点推断
Change point inference in high-dimensional regression models under temporal dependence
论文作者
论文摘要
本文关注的是，在高维线性回归时间序列上下文中，变化点估计器的限制分布，其中回归对象$（y_t，x_t）\ in \ Mathbb {r} \ times \ times \ times \ times \ mathbb {r}^p $在每个时间点$ t \ in \ in \ in \ in \ in \ in \ {1，n \ ldots，\ ldots，\ ldots，\ ldots，\ ldots，n \} $。在未知的时间点，称为变更点，回归系数变化，跳跃尺寸以$ \ ell_2 $ -norm的形式测量。我们在最小的跳跃大小消失并保持恒定的位置中提供了变化点估计器的限制分布。在功能依赖框架中，我们允许协变量和噪声序列在时间上取决于时间，这是在变化点推断文献中首次看到的。我们表明，在功能依赖性下，块类型的长期差异估计器是一致的，这有助于我们派生的限制分布的实际实现。我们还提出了一些我们分析的重要副产品，这些副产品具有他们自身的利益。这些包括动态编程算法的新型变体，以提高计算效率，时间依赖性下的一致变化点定位率以及具有功能依赖性的数据的新伯恩斯坦不平等。提供广泛的数值结果以支持我们的理论结果。提出的方法在R pankak \ texttt {changepoints} \ citep {changepoints_r}中实现。
This paper concerns about the limiting distributions of change point estimators, in a high-dimensional linear regression time series context, where a regression object $(y_t, X_t) \in \mathbb{R} \times \mathbb{R}^p$ is observed at every time point $t \in \{1, \ldots, n\}$. At unknown time points, called change points, the regression coefficients change, with the jump sizes measured in $\ell_2$-norm. We provide limiting distributions of the change point estimators in the regimes where the minimal jump size vanishes and where it remains a constant. We allow for both the covariate and noise sequences to be temporally dependent, in the functional dependence framework, which is the first time seen in the change point inference literature. We show that a block-type long-run variance estimator is consistent under the functional dependence, which facilitates the practical implementation of our derived limiting distributions. We also present a few important byproducts of our analysis, which are of their own interest. These include a novel variant of the dynamic programming algorithm to boost the computational efficiency, consistent change point localisation rates under temporal dependence and a new Bernstein inequality for data possessing functional dependence. Extensive numerical results are provided to support our theoretical results. The proposed methods are implemented in the R package \texttt{changepoints} \citep{changepoints_R}.
