Derivatives of the characteristic root of a synmetric or a hermitian matrix with two applications in multivariate analysis
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Publication:5674801
DOI10.1080/03610927308827036zbMath0259.62047OpenAlexW1979795581MaRDI QIDQ5674801
Publication date: 1973
Published in: Communications in Statistics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1080/03610927308827036
Multivariate distribution of statistics (62H10) Probability distributions: general theory (60E05) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Hermitian, skew-Hermitian, and related matrices (15B57)
Related Items (32)
Contributions to multivariate analysis by Professor Yasunori Fujikoshi ⋮ Matrix variate distribution theory under elliptical models -- V: the non-central Wishart and inverted Wishart distributions ⋮ On the distribution of the function of the F-matrix under an elliptical population ⋮ RAP-method (random perturbation method) for minimax \(G\)-filter ⋮ Asymptotic expansions for the distributions of latent roots of \(S_hS_e^{- 1}\) and of certain test statistics in MANOVA ⋮ An asymptotic expansion for the distributions of the latent roots of the Wishart matrix with multiple population roots ⋮ Asymptotic expansion for the distribution of a function of latent roots of the covariance matrix ⋮ Asymptotic behavior of the distributions of eigenvalues for beta-Wishart ensemble under the dispersed population eigenvalues ⋮ Distribution approximation of covariance matrix eigenvalues ⋮ An asymptotic expansion for the distribution of a function of latent roots of the noncentral Wishart matrix, when \(\Omega =0(n)\) ⋮ The asymptotic expansion of the distribution of Anderson's statistic for testing a latent vector of a covariance matrix ⋮ Improved approximations to distributions of the largest and the smallest latent roots of a Wishart matrix ⋮ Unnamed Item ⋮ Clustering rows and/or columns of a two-way contingency table and a related distribution theory ⋮ Fixed width confidence region for the mean of a multivariate normal distribution ⋮ Distribution of eigenvalues and eigenvectors of Wishart matrix when the population eigenvalues are infinitely dispersed and its application to minimax estimation of covariance matrix ⋮ Comparison of test statistics for the correlation coefficient inbivariate normal samples with type II censoring ⋮ Asymptotic distributions of the latent roots of the covariance matrix with multiple population roots ⋮ Partial differential equations for hypergeometric functions 3F2 of matrix argument ⋮ ASYMPTOTIC DISTRIBUTION OF THE LARGEST EIGENVALUE ⋮ Asymptotic expansions of the distributions of the latent roots and the latent vector of the Wishart and multivariate F matrices ⋮ Distributions of characteristic roots in multivariate analysis Part II. Non-Null Distribution ⋮ Partial differential equations for hypergeometric functions of complex argument matrices and their applications ⋮ Asymptotic expansions of the distributions of the latent roots in MANOVA and the canonical correlations ⋮ RAP-method (random perturbation method) for finding \(S\)-minimax control vectors and parameter estimates for some linear systems with random coefficients ⋮ Asymptotic expansions for the distributions of some functions of the latent roots of matrices in three situations ⋮ Asymptotic expansions for the distributions of functions of a correlation matrix ⋮ Asymptotic expansions for the distributions of statistics based on a correlation matrix ⋮ General saddlepoint approximations to distributions under an elliptical population ⋮ Delta method approach in a certain irregular condition ⋮ Second-order properties of a two-stage fixed-size confidence region when the covariance matrix has a structure ⋮ Maximum likelihood estimation and MUSIC in array localization signal processing: A review
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