Ellingson Leif, Groisser David, Osborne Daniel, Patrangenaru Vic, Schwartzman Armin
Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX.
Department of Mathematics, University of Florida, Gainesville, FL.
Commun Stat Simul Comput. 2017;46(6):4851-4879. doi: 10.1080/03610918.2015.1136413. Epub 2017 Feb 3.
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.
本文针对随机对称正定（SPD）矩阵的均值，根据两种不同度量提出了非参数双样本自助检验：一种是从SPD矩阵集嵌入欧几里得对称矩阵集中继承而来的弗罗贝尼乌斯（或欧几里得）度量，另一种是无需嵌入即可定义的规范度量，它建议进行内在分析。在后者的情况下，使用一种快速算法来计算自助内在均值。这些方法在模拟研究中得到了说明，并应用于诵读困难研究中从儿童注册DT图像的单个体素获得的扩散张量（DT）均值的两组比较。
