ArticleJournal of the Royal Statistical Society. Series B, Statistical methodology2012
Local Polynomial Regression for Symmetric Positive Definite Matrices.
Article in Journal of the Royal Statistical Society. Series B, Statistical methodology, 2012. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 9 papers.
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Who cites it
9 citing papers in PubMed.
- Wasserstein F-tests for Fréchet regression on Bures-Wasserstein manifolds.Journal of machine learning research : JMLR · 2025Article
- Statistical Learning Methods for Neuroimaging Data Analysis with Applications.Annual review of biomedical data science · 2023Review
- Geostatistical modeling of positive-definite matrices: An application to diffusion tensor imaging.Biometrics · 2022Article
- Conditional local distance correlation for manifold-valued data.Information processing in medical imaging : proceedings of the ... conference · 2017Article
- Regression Models on Riemannian Symmetric Spaces.Journal of the Royal Statistical Society. Series B, Statistical methodology · 2017Article
- Extrinsic local regression on manifold-valued data.Journal of the American Statistical Association · 2017Article
- FIBER DIRECTION ESTIMATION, SMOOTHING AND TRACKING IN DIFFUSION MRI.The annals of applied statistics · 2016Article
- VARYING COEFFICIENT MODEL FOR MODELING DIFFUSION TENSORS ALONG WHITE MATTER TRACTS.The annals of applied statistics · 2013Article
- Diffusion tensor smoothing through weighted Karcher means.Electronic journal of statistics · 2013Article
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Authors and funding
4 authors.
Funding
Abstract
Local polynomial regression has received extensive attention for the nonparametric estimation of regression functions when both the response and the covariate are in Euclidean space. However, little has been done when the response is in a Riemannian manifold. We develop an intrinsic local polynomial regression estimate for the analysis of symmetric positive definite (SPD) matrices as responses that lie in a Riemannian manifold with covariate in Euclidean space. The primary motivation and application of the proposed methodology is in computer vision and medical imaging. We examine two commonly used metrics, including the trace metric and the Log-Euclidean metric on the space of SPD matrices. For each metric, we develop a cross-validation bandwidth selection method, derive the asymptotic bias, variance, and normality of the intrinsic local constant and local linear estimators, and compare their asymptotic mean square errors. Simulation studies are further used to compare the estimators under the two metrics and to examine their finite sample performance. We use our method to detect diagnostic differences between diffusion tensors along fiber tracts in a study of human immunodeficiency virus.
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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.