Nonparametric two-sample tests on homogeneous Riemannian manifolds, Cholesky decompositions and Diffusion Tensor Image analysis

Daniel Osborne, Vic Patrangenaru, Leif Ellingson, David Groisser, Armin Schwartzman

Research output: Contribution to journalArticle

13 Scopus citations

Abstract

This paper addresses much needed asymptotic and nonparametric bootstrap methodology for two-sample tests for means on Riemannian manifolds with a simply transitive group of isometries. In particular, we develop a two-sample procedure for testing the equality of the generalized Frobenius means of two independent populations on the space of symmetric positive matrices. The new method naturally leads to an analysis based on Cholesky decompositions of covariance matrices which helps to decrease computational time and does not increase dimensionality. The resulting nonparametric matrix valued statistics are used for testing if there is a difference on average at a specific voxel between corresponding signals in Diffusion Tensor Images (DTIs) in young children with dyslexia when compared to their clinically normal peers, based on data that was previously analyzed using parametric methods.

Original languageEnglish
Pages (from-to)163-175
Number of pages13
JournalJournal of Multivariate Analysis
Volume119
DOIs
StatePublished - Aug 2013

Keywords

  • Cholesky decomposition
  • Diffusion Tensor Imaging
  • Generalized Frobenius metric
  • Nonparametric bootstrap
  • Nonparametric two sample tests
  • Primary
  • Riemannian homogeneous spaces
  • Secondary
  • Simply transitive groups
  • Symmetric positive-definite matrix

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