The Annals of Statistics

Multivariate varying coefficient model for functional responses

Hongtu Zhu, Runze Li, and Linglong Kong

Full-text: Open access

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.

Article information

Source
Ann. Statist., Volume 40, Number 5 (2012), 2634-2666.

Dates
First available in Project Euclid: 4 February 2013

Permanent link to this document
https://projecteuclid.org/euclid.aos/1359987533

Digital Object Identifier
doi:10.1214/12-AOS1045

Mathematical Reviews number (MathSciNet)
MR3097615

Zentralblatt MATH identifier
1373.62169

Subjects
Primary: 62G05: Estimation 62G08: Nonparametric regression
Secondary: 62G20: Asymptotic properties

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

Citation

Zhu, Hongtu; Li, Runze; Kong, Linglong. Multivariate varying coefficient model for functional responses. Ann. Statist. 40 (2012), no. 5, 2634--2666. doi:10.1214/12-AOS1045. https://projecteuclid.org/euclid.aos/1359987533


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