Regression Models on Riemannian Symmetric Spaces

Journal of the Royal Statistical Society. Series B, Statistical Methodology
Emil CorneaJoseph G Ibrahim

Abstract

The aim of this paper is to develop 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 arises frequently in medical imaging, surface modeling, and computer vision, among many others. 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.

References

Sep 2, 2004·IEEE Transactions on Medical Imaging·P Thomas FletcherSarang Joshi
Mar 22, 2007·Nature Reviews. Neuroscience·Lynn K PaulElliott H Sherr
Feb 23, 2010·Journal of the American Statistical Association·Hongtu ZhuWeili Lin
Mar 13, 2010·IEEE Transactions on Pattern Analysis and Machine Intelligence·Stephan HuckemannAxel Munk
Jul 4, 2012·Journal of Multivariate Analysis·Abhishek Bhattacharya, David Dunson
Dec 1, 2010·Biometrika·Abhishek Bhattacharya, David B Dunson
Sep 26, 2012·Journal of the Royal Statistical Society. Series B, Statistical Methodology·Ying YuanJ S Marron
Mar 1, 2012·Journal of the American Statistical Association·Xiaoyan ShiMartin Styner

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Citations

Jan 1, 2019·Journal of the American Statistical Association·Zhengwu ZhangDavid B Dunson
Oct 10, 2020·Biometrics·Xiongtao DaiHans-Georg Müller
Dec 11, 2020·Journal of the American Statistical Association·Wenliang PanJin Zhu

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