Distribution of the ratio of two Wishart matrices and cumulative probability evaluation by the holonomic gradient method

DOI10.1016/j.jmva.2018.01.002zbMath1397.62188arXiv1610.09187OpenAlexW2790130288MaRDI QIDQ1742747

Nobuki Takayama, Hiroki Hashiguchi, Akimichi Takemura

Publication date: 12 April 2018

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

Full work available at URL: https://arxiv.org/abs/1610.09187

zbMATH Keywords

Gröbner basis\(D\)-moduleszonal polynomialequality of covariance matricesRoy's maximum root testhypergeometric function of a matrix argument

Mathematics Subject Classification ID

Multivariate distribution of statistics (62H10) Asymptotic distribution theory in statistics (62E20) Hypothesis testing in multivariate analysis (62H15)

Related Items (3)

Expressing the largest eigenvalue of a singular beta F-matrix with heterogeneous hypergeometric functions ⋮ Heterogeneous hypergeometric functions with two matrix arguments and the exact distribution of the largest eigenvalue of a singular beta-Wishart matrix ⋮ Algebraic analysis of the hypergeometric function \(_1F_1\) of a matrix argument

Uses Software

• Risa/Asir
• hgm R

Cites Work

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• The efficient evaluation of the hypergeometric function of a matrix argument
• The holonomic gradient method for the distribution function of the largest root of a Wishart matrix
• Holonomic gradient descent and its application to the Fisher-Bingham integral
• On the exact finite series distribution of the smallest or the largest root of matrices in three situations
• Bessel functions of matrix argument
• Asymptotic expansions for the joint and marginal distributions of the latent roots of \(S_1S^{-1}_2\)
• One-sided test for the equality of two covariance matrices
• Computation of the null distribution of the largest or smallest latent roots of a beta matrix
• Gröbner Bases
• Methods of Multivariate Analysis
• System of Partial Differential Equations for the Hypergeometric Function 1F1 of a Matrix Argument on Diagonal Regions
• Some Distribution Problems Connected with the Characteristic Roots of $S_1S^{-1}_2$
• Systems of Partial Differential Equations for Hypergeometric Functions of Matrix Argument
• Distributions of Matrix Variates and Latent Roots Derived from Normal Samples

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