|MULTIVARIATE VARYING COEFFICIENT MODEL FOR FUNCTIONAL RESPONSES.
|Year of Publication
|Zhu, Hongtu, Runze Li, and Linglong Kong
|2012 Oct 01
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.
|Multivariate varying coefficient model for functional responses.
|PubMed Central ID
|P50 DA010075 / DA / NIDA NIH HHS / United States
U54 EB005149 / EB / NIBIB NIH HHS / United States
TL1 RR025745 / RR / NCRR NIH HHS / United States
R01 MH086633 / MH / NIMH NIH HHS / United States
R21 DA024260 / DA / NIDA NIH HHS / United States
UL1 RR025747 / RR / NCRR NIH HHS / United States
P01 CA142538 / CA / NCI NIH HHS / United States
KL2 RR025746 / RR / NCRR NIH HHS / United States
R21 AG033387 / AG / NIA NIH HHS / United States
MULTIVARIATE VARYING COEFFICIENT MODEL FOR FUNCTIONAL RESPONSES.