Asymptotic expansions for distributions of the large sample matrix resultant and related statistics on the Stiefel manifold

DOI10.1016/0047-259X(91)90101-7zbMath0739.62041MaRDI QIDQ1182761

Yasuko Chikuse

Publication date: 28 June 1992

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

zbMATH Keywords

von Mises-Fisher distributionStiefel manifoldasymptotic expansionsHermite polynomialsLaguerre polynomialsWishart distributionsLangevin distributionlocal alternative hypothesesmatrix-variate normal distributionsmatrix argumentshypothesis of uniformityinvariant-polynomials

Mathematics Subject Classification ID

Multivariate distribution of statistics (62H10) Asymptotic distribution theory in statistics (62E20) Characterization and structure theory for multivariate probability distributions; copulas (62H05) Applications of hypergeometric functions (33C90) Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable (33C50)

Related Items (9)

Hermite and Laguerre polynomials with complex matrix arguments ⋮ Edgeworth and saddle-point approximations for random rectangular matrices ⋮ Concentrated matrix Langevin distributions ⋮ Unnamed Item ⋮ Conjugate priors and posterior inference for the matrix Langevin distribution on the Stiefel manifold ⋮ Statistics on the Stiefel manifold: theory and applications ⋮ Density estimation on the Stiefel manifold ⋮ Bimatrix variate gamma-beta distributions ⋮ Procrustes analysis on some special manifolds

Cites Work

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• Bessel functions of matrix argument
• Large sample theory of the Langevin distribution
• Large sample theory for distributions on the hypersphere with rotational symmetries
• Distributions of orientations on Stiefel manifolds
• Invariant polynomials with two matrix arguments extending the zonal polynomials: Applications to multivariate distribution theory
• Uniform distribution on a Stiefel manifold
• Maximum likelihood estimators for the matrix von Mises-Fisher and Bingham distributions
• Multivariate calculation. Use of the continuous groups
• On the distribution of the latent roots of a positive definite random symmetric matrix. I
• The Distribution of Hotelling's Generalised $T_0^2$
• 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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