Asymptotic distributions of the latent roots with multiple population roots in multiple discriminant analysis
Copyright policy )Asymptotic distributions of the latent roots with multiple population roots in multiple discriminant analysis
Asymptotic expansions are derived for the confluent hypergeometric function1 F 1(a; c; R, S) with two argument matrices, which appears in the joint density function of the latent roots in multiple discriminant analysis, whenR is “large” and each of the latent roots ofR assumes the general multiplicity. Laplace's method and a partial differential equation method are utilized in the derivation.
multiple discriminant analysis, Classification and discrimination; cluster analysis (statistical aspects), Asymptotic distribution theory in statistics, Hypergeometric integrals and functions defined by them (\(E\), \(G\), \(H\) and \(I\) functions), joint density function of latent roots, partial differential equation method, noncentral Wishart, asymptotic distributions of latent roots, Multivariate distribution of statistics, confluent hypergeometric function, Laplace's method
multiple discriminant analysis, Classification and discrimination; cluster analysis (statistical aspects), Asymptotic distribution theory in statistics, Hypergeometric integrals and functions defined by them (\(E\), \(G\), \(H\) and \(I\) functions), joint density function of latent roots, partial differential equation method, noncentral Wishart, asymptotic distributions of latent roots, Multivariate distribution of statistics, confluent hypergeometric function, Laplace's method
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