2009/10/09 by Ian L. Dryden, Alexey Koloydenko, Diwei Zhou · 1 citation
Mathematics · #stat.AP
paper · pdf · doi:10.1214/09-aoas249
published as Annals of Applied Statistics 2009, Vol. 3, No. 3, 1102-1123 · Published in at http://dx.doi.org/10.1214/09-AOAS249 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)
arxiv created 2009/10/09 · arxiv updated 2009/12/01
The statistical analysis of covariance matrix data is considered and, in particular, methodology is discussed which takes into account the non-Euclidean nature of the space of positive semi-definite symmetric matrices. The main motivation for the work is the analysis of diffusion tensors in medical image analysis. The primary focus is on estimation of a mean covariance matrix and, in particular, on the use of Procrustes size-and-shape space. Comparisons are made with other estimation techniques, including using the matrix logarithm, matrix square root and Cholesky decomposition. Applications to diffusion tensor imaging are considered and, in particular, a new measure of fractional anisotropy called Procrustes Anisotropy is discussed.