10 papers
The joint density of top k sample eigenvectors and principal subspace inference
Koki Shimizu, Haoming Wang
In this paper, the exact joint density of the top sample eigenvectors is derived for any population covariance matrix , sample size , and $1 \l…
Multivariate normality test based on the uniform distribution on the Stiefel manifold
Koki Shimizu, Toshiya Iwashita
This study presents a new procedure for necessary tests of multivariate normality based on the uniform distribution on the Stiefel manifold. We demonstrate that the test statistic,…
Evaluating Singular Value Thresholds for DNN Weight Matrices based on Random Matrix Theory
Kohei Nishikawa, Koki Shimizu, Hiroki Hashiguchi
This study evaluates thresholds for removing singular values from singular value decomposition-based low-rank approximations of deep neural network weight matrices. Each weight mat…
Exact Distribution of the Noncentral Complex Roy's Largest Root Statistic via Pieri's Formula
Koki Shimizu, Hiroki Hashiguchi
In this study, we derive the exact distribution and moment of the noncentral complex Roy's largest root statistic, expressed as a product of complex zonal polynomials. We show that…
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…
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…