Open Access
October 2012 Multivariate varying coefficient model for functional responses
Hongtu Zhu, Runze Li, Linglong Kong
Ann. Statist. 40(5): 2634-2666 (October 2012). DOI: 10.1214/12-AOS1045


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.


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Hongtu Zhu. Runze Li. Linglong Kong. "Multivariate varying coefficient model for functional responses." Ann. Statist. 40 (5) 2634 - 2666, October 2012.


Published: October 2012
First available in Project Euclid: 4 February 2013

zbMATH: 1373.62169
MathSciNet: MR3097615
Digital Object Identifier: 10.1214/12-AOS1045

Primary: 62G05 , 62G08
Secondary: 62G20

Keywords: Functional response , global test statistic , multivariate varying coefficient model , simultaneous confidence band , weak convergence

Rights: Copyright © 2012 Institute of Mathematical Statistics

Vol.40 • No. 5 • October 2012
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