Computationally Efficient Change Detection for Functional Data

The detection of distributional shifts in functional data has become increasingly popular in recent years and has important applications in neuroscience. Over the past decade, many innovative 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. To increase computational efficiency and power, the dimensionality of the testing problem is reduced and a multiple testing correction is used. This results in a procedure that is not only computationally inexpensive but also allows us to test for differences in higher order moments of the factor loadings. Simulation studies are presented to demonstrate the validity of our approach. The proposed methodology is 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 (MS) patients.