Regression models on Riemannian symmetric spaces

• 成果类型: Article
• 署名作者: Cornea, Emil; Zhu, Hongtu; Kim, Peter; Ibrahim, Joseph G.
• 署名单位: University of North Carolina; University of North Carolina Chapel Hill; University of Guelph
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• 发表日期: 2017
• 页码: 463-482
• 关键词: extrinsic sample means; smoothing splines; corpus-callosum; least-squares; MANIFOLDS

摘要

The paper develops a general regression framework for the analysis of manifold-valued response in a Riemannian symmetric space (RSS) and its association with multiple covariates of interest, such as age or gender, in Euclidean space. Such RSS-valued data arise frequently in medical imaging, surface modelling and computer vision, among many other fields. We develop an intrinsic regression model solely based on an intrinsic conditional moment assumption, avoiding specifying any parametric distribution in RSS. We propose various link functions to map from the Euclidean space of multiple covariates to the RSS of responses. We develop a two-stage procedure to calculate the parameter estimates and determine their asymptotic distributions. We construct the Wald and geodesic test statistics to test hypotheses of unknown parameters. We systematically investigate the geometric invariant property of these estimates and test statistics. Simulation studies and a real data analysis are used to evaluate the finite sample properties of our methods.