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Updated: Jan 20, 2026

Diffusion Tensor Magnetic Resonance Imaging in the Analysis of Neurodegenerative Diseases
Published on: July 28, 2013
Nonparametric Bootstrap of Sample Means of Positive-Definite Matrices with an Application to Diffusion-Tensor-Imaging
Leif Ellingson1, David Groisser2, Daniel Osborne3
1Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX.
Abstract:
This paper presents nonparametric two-sample bootstrap tests formeans of randomsymmetric positivedefinite (SPD) matrices according to two differentmetrics: 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.
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