Distributions of orientations on Stiefel manifolds
Journal of Multivariate Analysis
High dimensional asymptotic expansions for the matrix Langevin distributions on the Stiefel manifold
Journal of Multivariate Analysis
Large sample asymptotic theory of tests for uniformity on the Grassmann manifold
Journal of Multivariate Analysis
Introduction to matrix analysis (2nd ed.)
Introduction to matrix analysis (2nd ed.)
Density estimation on the Stiefel Manifold
Journal of Multivariate Analysis
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This paper concerns the matrix Langevin distributions, exponential-type distributions defined on the two manifolds of our interest, the Stiefel manifold Vk,m and the manifold Pk,m-k of m × m orthogonal projection matrices idempotent of rank k which is equivalent to the Grassmann manifold Gk,m-k. Asymptotic theorems are derived when the concentration parameters of the distributions are large. We investigate the asymptotic behavior of distributions of some (matrix) statistics constructed based on the sample mean matrices in connection with testing hypotheses of the orientation parameters, and obtain asymptotic results in the estimation of large concentration parameters and in the classification of the matrix Langevin distributions.