Nonparametric bootstrap of sample means of positive-definite matrices with an application to diffusion-tensor-imaging data analysis

被引：4

作者：

Ellingson, Leif ^{[1
]}

Groisser, David ^{[2
]}

Osborne, Daniel ^{[3
]}

Patrangenaru, Vic ^{[4
]}

Schwartzman, Armin ^{[5
]}

机构：

[1] Texas Tech Univ, Dept Math & Stat, Lubbock, TX 79409 USA

[2] Univ Florida, Dept Math, Gainesville, FL 32611 USA

[3] Florida A&M Univ, Dept Math, Tallahassee, FL USA

[4] Florida State Univ, Dept Stat, Tallahasee, FL USA

[5] North Carolina State Univ, Dept Stat, Raleigh, NC USA

来源：

COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION | 2017年 / 46卷 / 06期

基金：

美国国家卫生研究院; 美国国家科学基金会;

关键词：

Center of mass; Diffusion tensor imaging; Extrinsic mean; Fast algorithms; Frechet mean; Intrinsic mean; Nonparametric bootstrap; CENTER-OF-MASS; MULTIVARIATE NORMALITY; DIRECTIONAL-DATA; SHAPE SPACES; STATISTICS; MANIFOLDS; GEOMETRY; MRI; IMAGES;

D O I：

10.1080/03610918.2015.1136413

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

This paper presents nonparametric two-sample bootstrap tests for means of random symmetric positive-definite (SPD) matrices according to two different metrics: the Frobenius (or Euclidean) metric, inherited from the embedding of the set of SPD metrics in the Euclidean set of symmetric matrices, and the canonical metric, which is defined without an embedding and suggests an intrinsic analysis. A fast algorithm is used to compute the bootstrap intrinsic means in the case of the latter. The methods are illustrated in a simulation study and applied to a two-group comparison of means of diffusion tensors (DTs) obtained from a single voxel of registered DT images of children in a dyslexia study.

引用

页码：4851 / 4879

页数：29

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