Testing Equality of Latent Functional Features Across Groups

Abstract

There are more and more applications of functional data analysis in recent years. Testing methodologies have received enormous attentions, especially in biomedical problems. The motivation of this work is to build statistical methodology for testing equality of functional data across groups. We concentrate on testing equality of the data structures based on latent features. The latent functional features are extracted from data by using a technique called Independent Component Analysis (ICA). GroupICA is modified version of ICA specifically for group inferences, and is applied in this work. After feature extraction, we perform our testing methods. Without much knowledge of data, bootstrapping and other data-driven testing procedures are considered, and we use Monte Carlo study to compare expected and empirical rejection levels. We use a modified Kolmogorov-Smirnov type statistics to test equality of marginal distributions of two or more stationary processes, and use spectral domain methods to develop a testing procedure for testing equality of second order dependence in those processes. In practice, we need the test to be robust against non-normal data, unknown dependence structure, different number of variables per group and unequal group sample sizes. We applied our methods in two bio-medical applications: 2D electrophoresis gels of protein and fMRI data analysis of simulated driving behavior.