In this article, we consider change point inference for high dimensional linear models. For change point detection, given any subgroup of variables, we propose a new method for testing the homogeneity of corresponding regression coefficients across the observations. Under some regularity conditions, the proposed new testing procedure controls the type I error asymptotically and is powerful against sparse alternatives and enjoys certain optimality. For change point identification, an argmax based change point estimator is proposed which is shown to be consistent for the true change point location. Moreover, combining with the binary segmentation technique, we further extend our new method for detecting and identifying multiple change points. Extensive numerical studies justify the validity of our new method and an application to the Alzheimer's disease data analysis further demonstrate its competitive performance.

翻译：本文考虑高维线性模型中的变点推断问题。针对变点检测，我们提出了一种新方法，用于检验任意变量子集对应的回归系数在观测值之间的同质性。在一定的正则条件下，所提出的新检验方法渐近地控制了第一类错误，对稀疏备择假设具有强大的检验功效，并具有某种最优性。针对变点识别，我们提出了一种基于argmax的变点估计量，并证明该估计量对真实变点位置具有一致性。此外，结合二元分割技术，我们进一步扩展了新方法以检测和识别多个变点。大量的数值研究验证了新方法的有效性，其在阿尔茨海默病数据分析中的应用进一步证明了其优越性能。