We propose a data segmentation methodology for the high-dimensional linear regression problem where the regression parameters are allowed to undergo multiple changes. The proposed methodology, MOSEG, proceeds in two stages where the data is first scanned for multiple change points using a moving window-based procedure, which is followed by a location refinement stage. MOSEG enjoys computational efficiency thanks to the adoption of a coarse grid in the first stage, as well as achieving theoretical consistency in estimating both the total number and the locations of the change points without requiring independence or sub-Gaussianity. We also propose MOSEG$.$MS, a multiscale extension of MOSEG which, while comparable to MOSEG in terms of computational complexity, achieves theoretical consistency for a broader parameter space that permits multiscale change points. We demonstrate good performance of the proposed methods in comparative simulation studies and in an application to to predicting the equity premium.

翻译：我们针对高维线性回归问题提出一种数据分割方法，其中回归参数允许发生多次变化。该方法称为MOSEG，分为两个阶段：首先通过基于滑动窗口的程序扫描数据以检测多个变点，随后进行位置精炼阶段。MOSEG因在第一阶段采用粗网格而兼具计算效率，且在无需独立性或次高斯性假设的前提下，能够理论一致地估计变点总数及其位置。我们还提出了MOSEG的多尺度扩展版本MOSEG$.$MS，该版本在计算复杂度上与MOSEG相当，但能在更广的参数空间（允许多尺度变点）中实现理论一致性。我们在对比模拟研究及一项股票溢价预测应用中验证了所提方法的良好性能。