WILD BINARY SEGMENTATION FOR MULTIPLE CHANGE-POINT DETECTION

• 成果类型: Article
• 署名作者: Fryzlewicz, Piotr
• 署名单位: University of London; London School Economics & Political Science
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/14-AOS1245
• 发表日期: 2014
• 页码: 2243-2281
• 关键词: least-squares estimation; number; algorithms; sequence; INFORMATION; criterion; selection; MODEL

摘要

We propose a new technique, called wild binary segmentation (WBS), for consistent estimation of the number and locations of multiple change-points in data. We assume that the number of change-points can increase to infinity with the sample size. Due to a certain random localisation mechanism, WBS works even for very short spacings between the change-points and/or very small jump magnitudes, unlike standard binary segmentation. On the other hand, despite its use of localisation, WBS does not require the choice of a window or span parameter, and does not lead to a significant increase in computational complexity. WBS is also easy to code. We propose two stopping criteria for WBS: one based on thresholding and the other based on what we term the 'strengthened Schwarz information criterion'. We provide default recommended values of the parameters of the procedure and show that it offers very good practical performance in comparison with the state of the art. The 'WBS methodology is implemented in the R package wbs, available on CRAN. In addition, we provide a new proof of consistency of binary segmentation with improved rates of convergence, as well as a corresponding result for WBS.