Multivariate varying coefficient model for functional responses

TL;DR

This paper introduces multivariate varying coefficient models (MVCM) for analyzing multiple functional responses in neuroimaging, providing inference procedures, theoretical properties, and applications to brain development data.

Contribution

The paper develops new statistical inference methods for MVCM, including convergence rates, hypothesis testing, and confidence bands, with theoretical validation and practical application.

Findings

Established asymptotic properties of coefficient estimates.

Proposed a global hypothesis test with known distribution.

Applied MVCM to neurodevelopmental imaging data.

Abstract

Motivated by recent work studying massive imaging data in the neuroimaging literature, we propose multivariate varying coefficient models (MVCM) for modeling the relation between multiple functional responses and a set of covariates. We develop several statistical inference procedures for MVCM and systematically study their theoretical properties. We first establish the weak convergence of the local linear estimate of coefficient functions, as well as its asymptotic bias and variance, and then we derive asymptotic bias and mean integrated squared error of smoothed individual functions and their uniform convergence rate. We establish the uniform convergence rate of the estimated covariance function of the individual functions and its associated eigenvalue and eigenfunctions. We propose a global test for linear hypotheses of varying coefficient functions, and derive its asymptotic distribution under the null hypothesis. We also propose a simultaneous confidence band for each individual effect curve. We conduct Monte Carlo simulation to examine the finite-sample performance of the proposed procedures. We apply MVCM to investigate the development of white matter diffusivities along the genu tract of the corpus callosum in a clinical study of neurodevelopment.