{"doi":"10.17615/ff4r-ag88","title":"Intrinsic Regression Models for Positive-Definite Matrices With Applications to Diffusion Tensor Imaging","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.","journal":"Carolina Digital Repository (University of North Carolina at Chapel Hill)","year":2020,"id":115196,"datarank":0.0,"base_score":0.0,"endowment":0.0,"self_citation_contribution":0.0,"citation_network_contribution":0.0,"self_endowment_contribution":0.0,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":3,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":0.9557,"is_data_producer":false,"deposit_databanks":null,"is_oa":true,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":"2020-01-01","fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":390426,"name":"Joseph G. Ibrahim","orcid":"0000-0003-2428-6552","position":1,"is_corresponding":false},{"id":399192,"name":"Yasheng Chen","orcid":"0000-0002-1133-452X","position":2,"is_corresponding":false},{"id":540804,"name":"C. Michael Hall","orcid":"0000-0002-7734-4587","position":3,"is_corresponding":false},{"id":314308,"name":"Weili Lin","orcid":"0000-0002-2900-8204","position":4,"is_corresponding":false},{"id":366143,"name":"Yimei Li","orcid":"0000-0001-9067-6992","position":5,"is_corresponding":false},{"id":14290,"name":"Hongtu Zhu","orcid":"0000-0002-6781-2690","position":0,"is_corresponding":true}],"reference_count":0,"raw_metadata":null,"created_at":"2026-07-18T23:13:36.820928Z","pmid":null,"pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}