Effective dimension reduction for sparse functional data

• 成果类型: Article
• 署名作者: Yao, F.; Lei, E.; Wu, Y.
• 署名单位: University of Toronto; North Carolina State University
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asv006
• 发表日期: 2015
• 页码: 421437
• 关键词: sliced inverse regression; models; SPACE

摘要

We propose a method of effective dimension reduction for functional data, emphasizing the sparse design where one observes only a few noisy and irregular measurements for some or all of the subjects. The proposed method borrows strength across the entire sample and provides a way to characterize the effective dimension reduction space, via functional cumulative slicing. Our theoretical study reveals a bias-variance trade-off associated with the regularizing truncation and decaying structures of the predictor process and the effective dimension reduction space. A simulation study and an application illustrate the superior finite-sample performance of the method.