Some properties of invariant polynomials with matrix arguments and their applications in econometrics

DOI10.1007/BF02482504zbMath0588.62074MaRDI QIDQ1073501

Yasuko Chikuse, A. W. Davis

Publication date: 1986

Published in: Annals of the Institute of Statistical Mathematics (Search for Journal in Brave)

zbMATH Keywords

invariant polynomialszonal polynomialsmatrix differential operatorsmatrix argumentsexpansions of the sum of independent noncentral Wishart matricesGeneralized Laguerre polynomialsgeneralized regression coefficient matrixk-class estimator

Mathematics Subject Classification ID

Multivariate distribution of statistics (62H10) Applications of statistics to economics (62P20) Multivariate analysis (62H99) Characterization and structure theory for multivariate probability distributions; copulas (62H05) Special functions (33-XX)

Related Items (17)

Appell's and Humbert's functions of matrix arguments ⋮ Hermite and Laguerre polynomials with complex matrix arguments ⋮ Generalized noncentral Hermite and Laguerre polynomials in multiple matrices ⋮ Matrix variate distribution theory under elliptical models -- V: the non-central Wishart and inverted Wishart distributions ⋮ Density estimation on the spaces of symmetric and rectangular matrices ⋮ Edgeworth and saddle-point approximations for random rectangular matrices ⋮ Exact expressions and numerical evaluation of average evolvability measures for characterizing and comparing \(\mathbf{G}\) matrices ⋮ Linear generalizations of various matric-t distributions ⋮ Noncentral bimatrix variate generalised beta distributions ⋮ Doubly noncentral singular matrix variate beta distributions ⋮ Invariant Polynomials and Related Tests ⋮ The Generalized Pascal Triangle and the Matrix Variate Jensen-Logistic Distribution ⋮ On the expectation of a ratio of quadratic forms in normal variables ⋮ Multivariate Meixner classes of invariant distributions ⋮ Complex bimatrix variate generalised beta distributions ⋮ Complex random matrices and Rician channel capacity ⋮ Exact densities for variance estimators of the structural disturbances in simultaneous equations models

Cites Work

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• On the Effects of Moderate Multivariate Nonnormality on Roy's Largest Root Test
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• The Distribution of the Latent Roots of the Covariance Matrix
• Distributions of Matrix Variates and Latent Roots Derived from Normal Samples
• Some Non-Central Distribution Problems in Multivariate Analysis

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