CHANGE-POINT ANALYSIS WITH IRREGULAR SIGNALS

• 成果类型: Article
• 署名作者: Kley, Tobias; Liu, Yuhan philip; Cao, Hongyuan; Wu, Wei biao
• 署名单位: University of Gottingen; University of Chicago; State University System of Florida; Florida State University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/24-AOS2451
• 发表日期: 2024
• 页码: 2913-2930
• 关键词: multiple change-points; threshold estimation; sequence; bootstrap; inference; relevant; tests

摘要

This paper considers the problem of testing and estimation of change point where signals after the change point can be highly irregular, which departs from the existing literature that assumes signals after the change point to be piecewise constant or vary smoothly. A two-step approach is proposed to effectively estimate the location of the change point. The first step consists of a preliminary estimation of the change point that allows us to obtain unknown parameters for the second step. In the second step, we use a new procedure to determine the position of the change point. We show that, under suitable conditions, the desirable OP(1) rate of convergence of the estimated change point can be obtained. We apply our method to analyze the Baidu search index of COVID-19 related symptoms and find December 8, 2019, to be the starting date of the COVID-19 pandemic.