Adaptive functional principal components analysis

• 成果类型: Article
• 署名作者: Wang, Sunny G. W.; Patilea, Valentin; Klutchnikoff, Nicolas
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Ecole Nationale de la Statistique et de l'Analyse de l'Information (ENSAI); Universite de Rennes; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Rennes
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1093/jrsssb/qkae106
• 发表日期: 2025
• 页码: 603-631
• 关键词: regression

摘要

Functional data analysis almost always involves smoothing discrete observations into curves, because they are never observed in continuous time and rarely without error. Although smoothing parameters affect the subsequent inference, data-driven methods for selecting these parameters are not well-developed, frustrated by the difficulty of using all the information shared by curves while being computationally efficient. On the one hand, smoothing individual curves in an isolated, albeit sophisticated way, ignores useful signals present in other curves. On the other hand, bandwidth selection by automatic procedures such as cross-validation after pooling all the curves together quickly become computationally unfeasible due to the large number of data points. In this paper, we propose a new data-driven, adaptive kernel smoothing, specifically tailored for functional principal components analysis through the derivation of sharp, explicit risk bounds for the eigen-elements. The minimization of these quadratic risk bounds provides refined, yet computationally efficient bandwidth rules for each eigen-element separately. Both common and independent design cases are allowed. Rates of convergence for the estimators are derived. An extensive simulation study, designed in a versatile manner to closely mimic the characteristics of real data sets supports our methodological contribution. An illustration on a real data application is provided.