Nonparametric two-sample tests on homogeneous Riemannian manifolds, Cholesky decompositions and diffusion tensor image analysis

DOI10.1016/j.jmva.2013.04.006zbMath1277.62127OpenAlexW2012361823WikidataQ115345766 ScholiaQ115345766MaRDI QIDQ391675

David Groisser, Armin Schwartzman, Leif Ellingson, Victor Patrangenaru, Daniel E. Osborne

Publication date: 10 January 2014

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmva.2013.04.006

zbMATH Keywords

Cholesky decompositiongeneralized Frobenius metricRiemannian homogeneous spacessimply transitive groupssymmetric positive-definite matrix

Mathematics Subject Classification ID

Related Items (12)

Evaluation and prediction of polygon approximations of planar contours for shape analysis ⋮ Nonparametric matrix regression function estimation over symmetric positive definite matrices ⋮ The location of a minimum variance squared distance functional ⋮ Overview of object oriented data analysis ⋮ Rates of the strong uniform consistency for the kernel-type regression function estimators with general kernels on manifolds ⋮ Lognormal Distributions and Geometric Averages of Symmetric Positive Definite Matrices ⋮ Two sample tests for mean 3D projective shapes from digital camera images ⋮ Riemannian Geometry of Symmetric Positive Definite Matrices via Cholesky Decomposition ⋮ Kriging prediction for manifold-valued random fields ⋮ Omnibus CLTs for Fréchet means and nonparametric inference on non-Euclidean spaces ⋮ Scaling-Rotation Distance and Interpolation of Symmetric Positive-Definite Matrices ⋮ Robustness of lognormal confidence regions for means of symmetric positive definite matrices when applied to mixtures of lognormal distributions

Cites Work

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• Minimax estimation for mixtures of Wishart distributions
• Random change on a Lie group and mean glaucomatous projective shape change detection from stereo pair images
• Nonparametric inference for extrinsic means on size-and-(reflection)-shape manifolds with applications in medical imaging
• Intrinsic statistics on Riemannian manifolds: Basic tools for geometric measurements
• Non-Euclidean statistics for covariance matrices, with applications to diffusion tensor imaging
• Inference for eigenvalues and eigenvectors of Gaussian symmetric matrices
• On the validity of the formal Edgeworth expansion
• Mean location and sample mean location on manifolds: Asymptotics, tests, confidence regions
• Constant gravitational fields and redshift of light
• Large sample theory of intrinsic and extrinsic sample means on manifolds. I
• Nonparametric comparison of mean directions or mean axes
• Deconvolution density estimation on \(\text{SO}(N)\)
• Newton's method, zeroes of vector fields, and the Riemannian center of mass
• Sharp adaptation for spherical inverse problems with applications to medical imaging
• False discovery rate analysis of brain diffusion direction maps
• A Riemannian framework for tensor computing
• Directions and projective shapes
• Locating Fréchet means with application to shape spaces
• Inference on 3D Procrustes Means: Tree Bole Growth, Rank Deficient Diffusion Tensors and Perturbation Models
• Riemannian $L^{p}$ center of mass: Existence, uniqueness, and convexity
• Asymptotic Minimax Bounds for Stochastic Deconvolution Over Groups
• Shape Manifolds, Procrustean Metrics, and Complex Projective Spaces
• Riemannian center of mass and mollifier smoothing
• Improved Pivotal Methods for Constructing Confidence Regions With Directional Data
• NEW LARGE SAMPLE AND BOOTSTRAP METHODS ON SHAPE SPACES IN HIGH LEVEL ANALYSIS OF NATURAL IMAGES
• A Differential Geometric Approach to the Geometric Mean of Symmetric Positive-Definite Matrices
• Nonparametric bootstrap of sample means of positive-definite matrices with an application to diffusion-tensor-imaging data analysis
• Geometric Means in a Novel Vector Space Structure on Symmetric Positive‐Definite Matrices
• Testing for uniformity on a compact homogeneous space
• Bootstrap Test for Difference Between Means in Nonparametric Regression
• The bootstrap and Edgeworth expansion

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