Nested Hypothesis Tests for Discovering Separability Structures in Multivariate Functional Data

Music City Center 

Notions of separability have frequently been utilized for tensor data, including random matrices and spatiotemporal data. Multivariate functional data in which the components share a common domain, such as regional BOLD signals in fMRI studies, constitute another important example. Separability of the covariance is a common structural assumption that leads to simplified computation and analysis. In recent years, two generalizations of separability have been proposed, namely weak and partial separability, where the latter is a further generalization of the former. This talk will outline a nonparametric nested testing procedure to aid in choosing one of these separability structures (or none at all) for a given data set. The tests for separability and weak separability are based on existing tests in the literature, while a novel test is proposed for assessing partial separability. Null distributions of the relevant test statistics are approximated via bootstrapping. Theoretical properties will be presented, along with an illustrative analysis on fMRI scans during a motor task.

Multivariate Functional Data

Separable Covariance

Nested Hypothesis Testing 

Section on Statistics in Imaging