α-separability and adjustable combination of amplitude and phase model for functional data

• 成果类型: Article
• 署名作者: Wang, Tian; Ding, Jimin
• 署名单位: Columbia University; Washington University (WUSTL)
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1093/jrsssb/qkae112
• 发表日期: 2025
• 页码: 746-771
• 关键词: maximum-likelihood-estimation; REGISTRATION; sample; Synchronization; alignment

摘要

We consider separating and joint modelling amplitude and phase variations for functional data in an identifiable manner. To rigorously address this separability issue, we introduce the notion of alpha-separability upon constructing a family of alpha-indexed metrics. We bridge alpha-separability with the uniqueness of Fr & eacute;chet mean, leading to the proposed adjustable combination of amplitude and phase model. The parameter alpha allows user-defined modelling emphasis between vertical and horizontal features and provides a novel viewpoint on the identifiability issue. We prove the consistency of the sample Fr & eacute;chet mean and variance, and the proposed estimators. Our method is illustrated in simulations and COVID-19 infection rate data.