PROFIT: Projection-based Test in Longitudinal Functional Data

Abstract

In many modern applications, a dependent functional response is observed for each subject over repeated time, leading to longitudinal functional data. In this paper, we propose a novel statistical procedure to test whether the mean function varies over time. Our approach relies on reducing the dimension of the response using data-driven orthogonal projections and it employs a likelihood-based hypothesis testing. We investigate the methodology theoretically and discuss a computationally efficient implementation. The proposed test maintains the type I error rate, and shows excellent power to detect departures from the null hypothesis in finite sample simulation studies. We apply our method to the longitudinal diffusion tensor imaging study of multiple sclerosis (MS) patients to formally assess whether the brain's health tissue, as summarized by fractional anisotropy (FA) profile, degrades over time during the study period.

References in corpus (6)

• Properties of principal component methods for functional and longitudinal data analysis
• Uniform convergence rates for nonparametric regression and principal component analysis in functional/longitudinal data
• Multilevel functional principal component analysis
• Statistical inferences for functional data
• A Kernel Two-Sample Test for Functional Data
• A test of weak separability for multi-way functional data, with application to brain connectivity studies

Cited by in corpus (1)

• A Frequency-Domain Approach for Integrating Multiple Functional Time Series