Distributions of orientations on Stiefel manifolds

DOI10.1016/0047-259X(90)90049-NzbMath0699.62050MaRDI QIDQ913412

Yasuko Chikuse

Publication date: 1990

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

zbMATH Keywords

decompositionsingular value decompositionHankel transformStiefel manifoldinvariant measuremaximum likelihood estimatorsorientationsRiemann spacesubspacesdifferential formvon Mises-Fishercomponent Stiefel manifoldshypergeometric functions of matrix argumentsmatrix Bingham distributionsmatrix Langevin distributionmodal orientationsampling distributions of matrix statistics

Mathematics Subject Classification ID

Multivariate distribution of statistics (62H10) Characterization and structure theory for multivariate probability distributions; copulas (62H05) Integration on manifolds; measures on manifolds (58C35) Classical hypergeometric functions, ({}_2F_1) (33C05)

Related Items (6)

Concentrated matrix Langevin distributions ⋮ Unnamed Item ⋮ The matrix angular central Gaussian distribution ⋮ Asymptotic expansions for distributions of the large sample matrix resultant and related statistics on the Stiefel manifold ⋮ Density estimation on the Stiefel manifold ⋮ High dimensional limit theorems and matrix decompositions on the Stiefel manifold

Cites Work

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• Bessel functions of matrix argument
• The matrix angular central Gaussian distribution
• Invariant polynomials with two matrix arguments extending the zonal polynomials: Applications to multivariate distribution theory
• An antipodally symmetric distribution on the sphere
• Maximum likelihood estimators for the matrix von Mises-Fisher and Bingham distributions
• Multivariate Meixner classes of invariant distributions
• Multivariate calculation. Use of the continuous groups
• Orientation statistics
• Distributions of Matrix Variates and Latent Roots Derived from Normal Samples
• Some Non-Central Distribution Problems in Multivariate Analysis
• Normal Multivariate Analysis and the Orthogonal Group

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