Regression Models on Riemannian Symmetric Spaces.

TitleRegression Models on Riemannian Symmetric Spaces.
Publication TypeJournal Article
Year of Publication2017
AuthorsCornea, Emil, Hongtu Zhu, Peter Kim, and Joseph G. Ibrahim
JournalJ R Stat Soc Series B Stat Methodol
Volume79
Issue2
Pagination463-482
Date Published2017 Mar
ISSN1369-7412
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.

DOI10.1111/rssb.12169
Alternate JournalJ R Stat Soc Series B Stat Methodol
Original PublicationRegression models on Riemannian symmetric spaces.
PubMed ID28529445
PubMed Central IDPMC5433528
Grant ListUL1 TR001111 / TR / NCATS NIH HHS / United States
UL1 TR002489 / TR / NCATS NIH HHS / United States
R01 MH086633 / MH / NIMH NIH HHS / United States
R01 GM070335 / GM / NIGMS NIH HHS / United States
T32 MH106440 / MH / NIMH NIH HHS / United States
P01 CA142538 / CA / NCI NIH HHS / United States
R21 AG033387 / AG / NIA NIH HHS / United States
R01 EB020426 / EB / NIBIB NIH HHS / United States