Approximating the matrix Fisher and Bingham distributions: Applications to spherical regression and Procrustes analysis

DOI10.1016/0047-259X(92)90072-NzbMath0746.62056OpenAlexW1987421743MaRDI QIDQ1192006

Donald St. P. Richards, Christopher Bingham, Theodore Chang

Publication date: 27 September 1992

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

Full work available at URL: https://doi.org/10.1016/0047-259x(92)90072-n

zbMATH Keywords

confidence regionapproximationsasymptotic expansionsHaar measureunit spherezonal polynomialsmaximum likelihood estimateProcrustes analysisBingham distributionunknown rotation\(O(p)\)\(SO(p)\)beef carcassesestimated rotationsEuclidean \(p\)-dimensional spaceexact conditional distributionhypergeometric functions of matrix argumentmatrix Fisher distributionsspherical regression modeltectonic plate reconstructions

Mathematics Subject Classification ID

Multivariate distribution of statistics (62H10) Asymptotic distribution theory in statistics (62E20) Foundations and philosophical topics in statistics (62A01) Applications of statistics (62P99) Applications of hypergeometric functions (33C90) Geological problems (86A60)

Related Items (5)

Entropy-based pivotal statistics for multi-sample problems in planar shape ⋮ A nonlinear mixed effects directional model for the estimation of the rotation axes of the human ankle ⋮ Distance-based tests for planar shape ⋮ A determinant representation for the distribution of quadratic forms in complex normal vectors ⋮ Laplace approximations for hypergeometric functions with matrix argument

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• Hypergeometric functions on complex matrix space
• Exponential transformation models
• Vector correlation
• Asymptotic Expansions for the Bingham Distribution
• An Asymptotic Expansion for the Noncentral Wishart Distribution
• Distributions of Matrix Variates and Latent Roots Derived from Normal Samples
• Spherical regression

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