Principal Component Analysis for Multivariate Functional Data

• Activity Number: 295
• Type: Topic Contributed
• Date/Time: Tuesday, August 6, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Jeng-Min Chiou*+
• Companies: Academia Sinica
• Keywords: Karhunen-Loeve expansion ; Multivariate analysis ; Normalization ; Principal component analysis

Abstract

Multivariate functional data contain multiple functional measurements that are recorded simultaneously. While functional principal component analysis has become a commonly used functional data method, we consider a normalization approach to functional principal component analysis for multivariate functional data. This procedure takes account of differences in units and reduces the effects of varying extent of variances between the multiple random functions. The method serves as a basic tool in dimension reduction for multivariate functional data, which share common functional principal component scores for realizations of the multiple random functions. We investigate the asymptotic properties for the estimated model components and demonstrate their finite sample performance and applications derived from the proposed method.