ArticleJournal of the American Statistical Association2009
Intrinsic Regression Models for Positive-Definite Matrices With Applications to Diffusion Tensor Imaging.
Article in Journal of the American Statistical Association, 2009. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 16 papers.
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Who cites it
16 citing papers in PubMed.
- EEG Motor Imagery Classification: Tangent Space with Gate-Generated Weight Classifier.Biomimetics (Basel, Switzerland) · 2024Article
- Geostatistical modeling of positive-definite matrices: An application to diffusion tensor imaging.Biometrics · 2022Article
- Network Modeling in Biology: Statistical Methods for Gene and Brain Networks.Statistical science : a review journal of the Institute of Mathematical Statistics · 2021Article
- Modeling Dynamic Functional Connectivity with Latent Factor Gaussian Processes.Advances in neural information processing systems · 2019Article
- Riemannian Nonlinear Mixed Effects Models: Analyzing Longitudinal Deformations in Neuroimaging.Proceedings. IEEE Computer Society Conference on Computer Vision and Pattern Recognition · 2017Article
- Riemannian Variance Filtering: An Independent Filtering Scheme for Statistical Tests on Manifold-valued Data.Conference on Computer Vision and Pattern Recognition Workshops. IEEE Computer Society Conference on Computer Vision and Pattern Recognition. Workshops · 2017Article
- Regression Models on Riemannian Symmetric Spaces.Journal of the Royal Statistical Society. Series B, Statistical methodology · 2017Article
- Nonparametric Bootstrap of Sample Means of Positive-Definite Matrices with an Application to Diffusion-Tensor-Imaging Data Analysis.Communications in statistics: Simulation and computation · 2017Article
- Lognormal Distributions and Geometric Averages of Symmetric Positive Definite Matrices.International statistical review = Revue internationale de statistique · 2016Article
- Manifold-valued Dirichlet Processes.JMLR workshop and conference proceedings · 2015Article
- Canonical Correlation Analysis on Riemannian Manifolds and Its Applications.Computer vision - ECCV ... : ... European Conference on Computer Vision : proceedings. European Conference on Computer Vision · 2014Article
- VARYING COEFFICIENT MODEL FOR MODELING DIFFUSION TENSORS ALONG WHITE MATTER TRACTS.The annals of applied statistics · 2013Article
- Semiparametric Bayesian local functional models for diffusion tensor tract statistics.NeuroImage · 2012Article
- Local Polynomial Regression for Symmetric Positive Definite Matrices.Journal of the Royal Statistical Society. Series B, Statistical methodology · 2012Article
- FADTTS: functional analysis of diffusion tensor tract statistics.NeuroImage · 2011Article
- FRATS: Functional Regression Analysis of DTI Tract Statistics.IEEE transactions on medical imaging · 2010Article
Corrections and comments
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Authors and funding
6 authors.
Funding
Abstract
The aim of this paper is to develop an intrinsic regression model for the analysis of positive-definite matrices as responses in a Riemannian manifold and their association with a set of covariates, such as age and gender, in a Euclidean space. The primary motivation and application of the proposed methodology is in medical imaging. Because the set of positive-definite matrices do not form a vector space, directly applying classical multivariate regression may be inadequate in establishing the relationship between positive-definite matrices and covariates of interest, such as age and gender, in real applications. Our intrinsic regression model, which is a semiparametric model, uses a link function to map from the Euclidean space of covariates to the Riemannian manifold of positive-definite matrices. We develop an estimation procedure to calculate parameter estimates and establish their limiting distributions. We develop score statistics to test linear hypotheses on unknown parameters and develop a test procedure based on a resampling method to simultaneously assess the statistical significance of linear hypotheses across a large region of interest. Simulation studies are used to demonstrate the methodology and examine the finite sample performance of the test procedure for controlling the family-wise error rate. We apply our methods to the detection of statistical significance of diagnostic effects on the integrity of white matter in a diffusion tensor study of human immunodeficiency virus. Supplemental materials for this article are available online.
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Registered trials
Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.