Asymptotic solutions of the hypergeometric function \(_1F_1\) of matrix argument, useful in multivariate analysis

DOI10.1007/BF02479780zbMath0314.62023MaRDI QIDQ1220773

Nariaki Sugiura

Publication date: 1972

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

Mathematics Subject Classification ID

Multivariate distribution of statistics (62H10) Hypothesis testing in multivariate analysis (62H15) Theoretical approximation in context of PDEs (35A35) Classical hypergeometric functions, ({}_2F_1) (33C05)

Related Items (4)

Likelihood ratio tests for elaborate covariance structures and for MANOVA models with elaborate covariance structures -- a review ⋮ Partial differential equations for hypergeometric functions ₃F₂ of matrix argument ⋮ Asymptotic formulas for the hypergeometric function \(_2F_1\) of matrix argument, useful in multivariate analysis ⋮ Recurrence relations of coefficients of the generalized hypergeometric function in multivariate analysis

Cites Work

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• Further asymptotic formulas for the non-null distributions of three statistics for multivariate linear hypothesis
• Asymptotic expansion of the distribution of the generalized variance for noncentral Wishart matrix, when \(\Omega= O(n)\)
• Asymptotic Expansions of the Non-Null Distributions of the Likelihood Ratio Criteria for Multivariate Linear Hypothesis and Independence
• Asymptotic Distributions of Some Multivariate Tests
• Systems of Partial Differential Equations for Hypergeometric Functions of Matrix Argument
• Some Non-Central Distribution Problems in Multivariate Analysis

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