JSM 2011 Online Program

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Abstract Details

Activity Number: 127
Type: Contributed
Date/Time: Monday, August 1, 2011 : 8:30 AM to 10:20 AM
Sponsor: Section on Nonparametric Statistics
Abstract - #301786
Title: Analysis of Longitudinal Data with Multiple Response Functions
Author(s): Jeng-Min Chiou*+
Companies: Academia Sinica
Address: 128 Sec 2 Academia Road, Taipei, International, 11529, Taiwan
Keywords: Functional data analysis ; Linear manifold ; Traffic flow analysis ; Varying coefficient functions
Abstract:

We propose a linear manifold modeling method of exploring dependency relationship between multiple random processes in longitudinal data. The linear manifold is defined through a set of data-determined linear combinations for the multiple component trajectories, subject to the condition that their variances are relatively small. The model is characterized by a set of varying coefficient functions under orthonormality constraints, leading to time-varying relationships between the multiple functional components. Under mild conditions, the integral of the linear manifold model variances can be expressed in a quadratic form, which facilitates the construction of the model. This linear manifold modeling approach provides a tool for determining a set of linear relationships that govern the components of multiple random functions, and further yields noise-reduced multivariate component trajectories. The proposed approach is illustrated through an application to highway traffic flow analysis, where the linear manifold describes the relationships between the multiple functional measurements.


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