On functional processes with multiple discontinuities

• 成果类型: Article
• 署名作者: Li, Jialiang; Li, Yaguang; Hsing, Tailen
• 署名单位: National University of Singapore; Chinese Academy of Sciences; University of Science & Technology of China, CAS; University of Michigan System; University of Michigan
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12493
• 发表日期: 2022
• 页码: 933-972
• 关键词: change-point estimation; term structure; factor models; regression; SPARSE; CONVERGENCE; estimators; inference; TRENDS; rates

摘要

We consider the problem of estimating multiple change points for a functional data process. There are numerous examples in science and finance in which the process of interest may be subject to some sudden changes in the mean. The process data that are not in a close vicinity of any change point can be analysed by the usual nonparametric smoothing methods. However, the data close to change points and contain the most pertinent information of structural breaks need to be handled with special care. This paper considers a half-kernel approach that addresses the inference of the total number, locations and jump sizes of the changes. Convergence rates and asymptotic distributional results for the proposed procedures are thoroughly investigated. Simulations are conducted to examine the performance of the approach, and a number of real data sets are analysed to provide an illustration.