Automatic Detection of Significant Areas for Functional Data with Directional Error Control

TL;DR

This paper introduces a nonparametric Gaussian process regression method for automatically detecting significant sub-areas in functional data, controlling directional false discovery rates, with applications in medical research.

Contribution

It develops an optimal, computationally efficient procedure for large-scale multiple testing in functional data analysis that controls directional false discovery rates asymptotically.

Findings

Procedure effectively controls false discovery rates in simulations.

Method is computationally inexpensive and adaptable to different observation time points.

Successfully applied to real-world data in cerebral palsy research.

Abstract

To detect differences between the mean curves of two samples in longitudinal study or functional data analysis, we usually need to partition the temporal or spatial domain into several pre-determined sub-areas. In this paper we apply the idea of large-scale multiple testing to find the significant sub-areas automatically in a general functional data analysis framework. A nonparametric Gaussian process regression model is introduced for two-sided multiple tests. We derive an optimal test which controls directional false discovery rates and propose a procedure by approximating it on a continuum. The proposed procedure controls directional false discovery rates at any specified level asymptotically. In addition, it is computationally inexpensive and able to accommodate different time points for observations across the samples. Simulation studies are presented to demonstrate its finite sample performance. We also apply it to an executive function research in children with Hemiplegic Cerebral Palsy and extend it to the equivalence tests.