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Nonparametric bootstrap of sample means of positive-definite matrices with an application to diffusion-tensor-imaging data analysis |
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| Authors: | Leif Ellingson David Groisser Daniel Osborne Vic Patrangenaru Armin Schwartzman |
| Affiliation: | 1. Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX, USA;2. Department of Mathematics, University of Florida, Gainesville, FL, USA;3. Department of Mathematics, Florida Agricultural and Mechanical University, Tallahassee, FL, USA;4. Department of Statistics, Florida State University, Tallahasee, FL, USA;5. Department of Statistics, North Carolina State University, Raleigh, NC, USA |
| Abstract: | 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. |
| Keywords: | Center of mass Diffusion tensor imaging Extrinsic mean Fast algorithms Fréchet mean Intrinsic mean Nonparametric bootstrap |