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

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. Fast algorithms are used to compute the bootstrap instrinsic means in the case of the latter. The methods are illustrated in 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. Short title: Nonparametric Data Analysis for SPD Matrices