CONSISTENT SELECTION OF THE NUMBER OF CHANGE-POINTS VIA SAMPLE-SPLITTING

• 成果类型: Article
• 署名作者: Zou, Changliang; Wang, Guanghui; Li, Runze
• 署名单位: Nankai University; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/19-AOS1814
• 发表日期: 2020
• 页码: 413-439
• 关键词: nonparametric approach; information criterion; model selection; multiple; maximum; identification

摘要

In multiple change-point analysis, one of the major challenges is to estimate the number of change-points. Most existing approaches attempt to minimize a Schwarz information criterion which balances a term quantifying model fit with a penalization term accounting for model complexity that increases with the number of change-points and limits overfitting. However, different penalization terms are required to adapt to different contexts of multiple change-point problems and the optimal penalization magnitude usually varies from the model and error distribution. We propose a data-driven selection criterion that is applicable to most kinds of popular change-point detection methods, including binary segmentation and optimal partitioning algorithms. The key idea is to select the number of change-points that minimizes the squared prediction error, which measures the fit of a specified model for a new sample. We develop a cross-validation estimation scheme based on an order-preserved sample-splitting strategy, and establish its asymptotic selection consistency under some mild conditions. Effectiveness of the proposed selection criterion is demonstrated on a variety of numerical experiments and real-data examples.