Detecting Distributional Shifts in Functional Data

• Activity Number: 512
• Type: Contributed
• Date/Time: Wednesday, August 1, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Gina-Maria Pomann*+ and Ana-Maria Staicu and Sujit Kumar Ghosh
• Companies: North Carolina State University and North Carolina State University and North Carolina State University
• Keywords: Functional Data Analysis ; Common Functional Principal Components ; Change Detection ; Two Sample Problem

Abstract

The detection of distributional shifts in functional data has become increasingly popular in recent years and has numerous applications in neuroscience. Methodologies have been developed within the framework of functional principal component analysis to detect differences in the mean functions, eigenfunctions, and the variance of the factor loadings. We extend some of these functional principal components-based methods by developing a test for the equality of the distributions of two samples of curves, when their eigenfunctions are the same. Our approach reduces the dimensionality of the testing problem in a way that enables the application of traditional nonparametric univariate testing procedures. This results in a procedure that is not only computationally inexpensive, but also allows us to extend the testing of the variance of factor loadings to higher order moments. Simulation studies are presented to demonstrate the validity of our approach. The proposed methodology is then illustrated by applying it to a state-of-the art diffusion tensor imaging (DTI) study, where the objective is to compare white matter tract profiles in healthy individuals and multiple sclerosis patients.