标题： 层次变化点检测的多变量时间序列通过球检测函数 显示英文标题

标题： Hierarchical Change-Point Detection for Multivariate Time Series via a Ball Detection Function

摘要： 随机对象序列来源于许多实际应用，包括高通量组学数据和功能成像数据。 这些序列通常是依赖的、非线性的，甚至是非欧几里得的，一个重要问题是在这种依赖序列的巴拿赫空间或度量空间中检测变化点。 这个问题通常需要准确推断不仅是否发生了变化，而且当变化确实发生时，变化的位置在哪里。 为此，我们首先介绍了一个球检测函数，并证明如果序列只有一个变化点，该函数会在变化点处达到最大值。 此外，我们提出了一个一致估计的球检测函数，基于此我们开发了一种分层算法来检测所有可能的变化点。 我们证明了估计的变化点位置是一致的。 我们的方法可以在不假设任何特定类型的变化点的情况下估计变化点的数量并检测它们的位置，因为序列中的变化可以以不同的方式发生。 大量的仿真研究和对两个有趣的真实数据集（风向和比特币价格）的分析表明，与现有的竞争对手相比，我们的方法具有显著的优势，特别是在数据是非欧几里得或方差存在分布变化时。 显示英文摘要

摘要： Sequences of random objects arise from many real applications, including high throughput omic data and functional imaging data. Those sequences are usually dependent, non-linear, or even Non-Euclidean, and an important problem is change-point detection in such dependent sequences in Banach spaces or metric spaces. The problem usually requires the accurate inference for not only whether changes might have occurred but also the locations of the changes when they did occur. To this end, we first introduce a Ball detection function and show that it reaches its maximum at the change-point if a sequence has only one change point. Furthermore, we propose a consistent estimator of Ball detection function based on which we develop a hierarchical algorithm to detect all possible change points. We prove that the estimated change-point locations are consistent. Our procedure can estimate the number of change-points and detect their locations without assuming any particular types of change-points as a change can occur in a sequence in different ways. Extensive simulation studies and analyses of two interesting real datasets wind direction and Bitcoin price demonstrate that our method has considerable advantages over existing competitors, especially when data are non-Euclidean or when there are distributional changes in the variance.