标题： 二值分割在功能数据多变点估计中的一致性 显示英文标题

标题： Consistency of Binary Segmentation For Multiple Change-Points Estimation With Functional Data

摘要： 对于在均值函数中表现出多个变化点的顺序观测功能数据，我们基于功能CUSUM过程的范数和标准二分法，建立了估计的变化点数量和位置的一致性结果。 除了将Venkatraman（1992）和Fryzlewicz（2014）针对标量数据的类似结果扩展到一般的希尔伯特空间设置外，我们的主要结果是在不假设数据正态性的条件下，并在模型误差的一般线性过程条件下建立的。 显示英文摘要

摘要： For sequentially observed functional data exhibiting multiple change points in the mean function, we establish consistency results for the estimated number and locations of the change points based on the norm of the functional CUSUM process and standard binary segmentation. In addition to extending similar results in Venkatraman (1992) and Fryzlewicz (2014) for scalar data to the general Hilbert space setting, our main results are established without assuming the Gaussianity of the data, and under general linear process conditions on the model errors.