9 papers
Chi-square approximation for the distribution of individual eigenvalues of a singular Wishart matrix
Koki Shimizu, Hiroki Hashiguchi
This paper discusses the approximate distributions of eigenvalues of a singular Wishart matrix. We give the approximate joint density of eigenvalues by Laplace approximation for th…
Numerical computation for the exact distribution of Roy's largest root statistic under linear alternative
Koki Shimizu, Hiroki Hashiguchi
This paper discusses the computation of exact powers for Roy's test in multivariate analysis of variance~(MANOVA). We derive an exact expression for the largest eigenvalue of a sin…
Algorithm for the product of Jack polynomials and its application to the sphericity test
Koki Shimizu, Hiroki Hashiguchi
In this study, we derive the density and distribution function of a ratio of the largest and smallest eigenvalues of a singular beta-Wishart matrix for the sphericity test. These f…
Generalized heterogeneous hypergeometric functions and the distribution of the largest eigenvalue of an elliptical Wishart matrix
Aya Shinozaki, Koki Shimizu, Hiroki Hashiguchi
In this study, we derive the exact distributions of eigenvalues of a singular Wishart matrix under an elliptical model. We define generalized heterogeneous hypergeometric functions…
Approximation to probability density functions in sampling distributions based on Fourier cosine series
Shigekazu Nakagawa, Hiroki Hashiguchi, Yoko Ono
We derive a simple and precise approximation to probability density functions in sampling distributions based on the Fourier cosine series. After clarifying the required conditions…
Expressing the largest eigenvalue of a singular beta F-matrix with heterogeneous hypergeometric functions
Koki Shimizu, Hiroki Hashiguchi
In this paper, the exact distribution of the largest eigenvalue of a singular random matrix for multivariate analysis of variance (MANOVA) is discussed. The key to developing the d…
Heterogeneous hypergeometric functions with two matrix arguments and the exact distribution of the largest eigenvalue of a singular beta-Wishart matrix
Koki Shimizu, Hiroki Hashiguchi
This paper discusses certain properties of heterogeneous hypergeometric functions with two matrix arguments. These functions are newly defined but have already appeared in statisti…
Distribution of ratio of two Wishart matrices and evaluation of cumulative probability by holonomic gradient method
Hiroki Hashiguchi, Nobuki Takayama, Akimichi Takemura
We study the distribution of the ratio of two central Wishart matrices with different covariance matrices. We first derive the density function of a particular matrix form of the r…
A measure of skewness for testing departures from normality
Shigekazu Nakagawa, Hiroki Hashiguchi, Naoto Niki
We propose a new skewness test statistic for normality based on the Pearson measure of skewness. We obtain asymptotic first four moments of the null distribution for this statistic…