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Motivated by recent work studying massive imaging data in the neuroimagingliterature, we propose multivariate varying coefficient models (MVCM) formodeling the relation between multiple functional responses and a set ofcovariates. We develop several statistical inference procedures for MVCM andsystematically study their theoretical properties. We first establish the weakconvergence of the local linear estimate of coefficient functions, as well asits asymptotic bias and variance, and then we derive asymptotic bias and meanintegrated squared error of smoothed individual functions and their uniformconvergence rate. We establish the uniform convergence rate of the estimatedcovariance function of the individual functions and its associated eigenvalueand eigenfunctions. We propose a global test for linear hypotheses of varyingcoefficient functions, and derive its asymptotic distribution under the nullhypothesis. We also propose a simultaneous confidence band for each individualeffect curve. We conduct Monte Carlo simulation to examine the finite-sampleperformance of the proposed procedures. We apply MVCM to investigate thedevelopment of white matter diffusivities along the genu tract of the corpuscallosum in a clinical study of neurodevelopment.

Multivariate varying coefficient model for functional responses