Analysis of Multiple Random Functions via Dynamic Constraints

• Activity Number: 176
• Type: Contributed
• Date/Time: Monday, August 2, 2010 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Jeng-Min Chiou*+ and Hans-Georg Mueller
• Companies: Academia Sinica and University of California, Davis
• Keywords: Functional data analysis ; Multiple random functions ; Orthogonal least squares ; Principal components ; Traffic flow ; Varying coefficients

Abstract

Time-dynamic dependency between the components of multiple random trajectories is of interest. To explore dynamic relationship between component trajectories, we propose to use data-adaptive functional constraints, which comprise a set of linear combinations of the transformed functional components that have relatively small variances. The component coefficient functions of the constraints form an orthonormal set, which can be effectively constructed by adopting an orthogonal least squares approach based on principal component analysis. This approach provides a tool for determining constraints that govern the components of multivariate random functions, thus also obtaining the effective dimension of the observed system. The proposed methods are illustrated with an application to traffic flow analysis for the longitudinally recorded multiple traffic parameters.