A2050
Title: Change-point detection for object-valued time series
Authors: Changbo Zhu - University of Notre Dame (United States) [presenting]
Abstract: Change point detection is addressed for object-valued data residing in a metric space, a topic that has attracted recent interest. Existing methods either focus on independent data or can only detect changes in the Frechet mean or variance. A self-normalization (SN) based statistic is proposed for detecting shifts in the marginal distribution of object-valued time series. The test is universally applicable to a wide range of object-valued data, such as distributional and network data, and accommodates weak serial dependence. The proposed test statistic is nearly tuning parameter free, has a pivotal limiting null distribution, and uses only pairwise distances. When combined with the Wild Binary Segmentation (WBS) algorithm, the statistic can estimate the number and locations of multiple change points. Asymptotic results for the SN-based statistic are derived under both null and local alternatives in the single change point setting. The WBS estimation consistency is established for a broad class of object-valued time series in a nonparametric setting, requiring new non-standard theoretical arguments. Extensive numerical experiments and real data analysis demonstrate the effectiveness and broad applicability of the proposed method.
