Inference for eigenvalues and eigenvectors in exponential families of random symmetric matrices

JOURNAL OF MULTIVARIATE ANALYSIS

卷:162

Article

Lee, Han Na¹  Schwartzman, Armin² 

[1] North Carolina State Univ, Dept Stat, 2311 Stinson Dr, Raleigh, NC 27695 USA

[2] Univ Calif San Diego, Div Biostat, 9500 Gilman Dr,MC0631, La Jolla, CA 92093 USA

关键词: Diffusion tensor imaging (DTI);    Matrix-variate Gamma distribution;    Statistics on manifolds;    Symmetric positive definite matrices;    Wishart distribution;   

DOI  :  10.1016/j.jmva.2017.08.006

来源: Elsevier

【 摘 要 】

Diffusion tensor imaging (DTI) data consist of a 3 x 3 positive definite random matrix at every voxel. Motivated by the anatomical interpretation of the data, we define a matrix-variate exponential family of distributions for random positive definite matrices and develop estimation and testing procedures for the eigenstructure of the mean parameter. The exponential family includes the spherical Gaussian and matrix-Gamma distributions as special cases. Maximum likelihood estimation and likelihood ratio testing procedures are carried out both in the one-sample and two-sample problems. In addition to their large-samplebehavior, their non-asymptotic performance is evaluated via simulations. The methods are illustrated in a real DTI data example. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

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