TY - JOUR
T1 - Spatially Varying Coefficient Model for Neuroimaging Data With Jump Discontinuities
AU - Zhu, Hongtu
AU - Fan, Jianqing
AU - Kong, Linglong
N1 - Funding Information:
Hongtu Zhu is Professor of Biostatistics, Department of Biostatistics, University of North Carolina at Chapel Hill, NC 27599-7420 (E-mail: hzhu@bios.unc.edu). Jianqing Fan is Frederick L. Moore’18 Professor of Finance, Department of Operational Research and Finance Engineering, Princeton University, Princeton, NJ 08544, and Honorary Professor, Academy of Mathematical and System Science, Chinese Academy of Science, Beijing, China (E-mail: jqfan@princeton.edu). Linglong Kong is Assistant Professor of Statistics, Department of Mathematics and Statistics, University of Alberta, Canada, Edmonton, AB Canada T6G 2G1 (E-mail: lkong@ualberta.ca). Dr. Zhu was supported by NIH grants RR025747-01, P01CA142538-01, MH086633, and EB005149-01. Dr. Fan was supported by NSF grant DMS-1206464 and NIH grants R01-GM072611 and R01GM100474. Dr. Kong was supported by NSERC-RGPIN. The content is solely the responsibility of the authors and does not necessarily represent the official views of the NSF or the NIH. The authors thank the Editor, the Associate Editor, and two anonymous referees for valuable suggestions, which greatly helped to improve our presentation.
Publisher Copyright:
© 2014 American Statistical Association.
PY - 2014/9
Y1 - 2014/9
N2 - Motivated by recent work on studying massive imaging data in various neuroimaging studies, we propose a novel spatially varying coefficient model (SVCM) to capture the varying association between imaging measures in a three-dimensional volume (or two-dimensional surface) with a set of covariates. Two stylized features of neuorimaging data are the presence of multiple piecewise smooth regions with unknown edges and jumps and substantial spatial correlations. To specifically account for these two features, SVCM includes a measurement model with multiple varying coefficient functions, a jumping surface model for each varying coefficient function, and a functional principal component model. We develop a three-stage estimation procedure to simultaneously estimate the varying coefficient functions and the spatial correlations. The estimation procedure includes a fast multiscale adaptive estimation and testing procedure to independently estimate each varying coefficient function, while preserving its edges among different piecewise-smooth regions. We systematically investigate the asymptotic properties (e.g., consistency and asymptotic normality) of the multiscale adaptive parameter estimates. We also establish the uniform convergence rate of the estimated spatial covariance function and its associated eigenvalues and eigenfunctions. Our Monte Carlo simulation and real-data analysis have confirmed the excellent performance of SVCM. Supplementary materials for this article are available online.
AB - Motivated by recent work on studying massive imaging data in various neuroimaging studies, we propose a novel spatially varying coefficient model (SVCM) to capture the varying association between imaging measures in a three-dimensional volume (or two-dimensional surface) with a set of covariates. Two stylized features of neuorimaging data are the presence of multiple piecewise smooth regions with unknown edges and jumps and substantial spatial correlations. To specifically account for these two features, SVCM includes a measurement model with multiple varying coefficient functions, a jumping surface model for each varying coefficient function, and a functional principal component model. We develop a three-stage estimation procedure to simultaneously estimate the varying coefficient functions and the spatial correlations. The estimation procedure includes a fast multiscale adaptive estimation and testing procedure to independently estimate each varying coefficient function, while preserving its edges among different piecewise-smooth regions. We systematically investigate the asymptotic properties (e.g., consistency and asymptotic normality) of the multiscale adaptive parameter estimates. We also establish the uniform convergence rate of the estimated spatial covariance function and its associated eigenvalues and eigenfunctions. Our Monte Carlo simulation and real-data analysis have confirmed the excellent performance of SVCM. Supplementary materials for this article are available online.
KW - Asymptotic normality
KW - Functional principal component analysis
KW - Jumping surface model
KW - Kernel
KW - Wald test
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U2 - 10.1080/01621459.2014.881742
DO - 10.1080/01621459.2014.881742
M3 - Article
C2 - 25435598
AN - SCOPUS:84907527507
SN - 0162-1459
VL - 109
SP - 1084
EP - 1098
JO - Journal of the American Statistical Association
JF - Journal of the American Statistical Association
IS - 507
ER -