Covering statistical analysis on the two special manifolds, the Stiefel manifold and the Grassmann manifold, this book is designed as a reference for both theoretical and applied statisticians. It will also be used as a textbook for a graduate course in multivariate analysis. It is assumed that the reader is familiar with the usual theory of univariate statistics and a thorough background in mathematics, in particular, knowledge of multivariate calculation techniques.

Leseprobe

The Special Manifolds and Related Multivariate Topics * Distributions on the Special Manifolds * Decompositions of the Special Manifolds * Distributional Problems in the Decomposition Theorems and the Sampling Theory * The Inference on the Parameters of the Matrix Langevin Distributions * Large Sample Asymptotic Theorems in Connection with Tests for Uniformity * Asymptotic Theorems for Concentrated Matrix Langevin Distributions * High Dimensional Asymptotic Theorems * Procrustes Analysis on the Special Manifolds * Density Estimation on the Special Manifolds * Measures of Orthogonal Association on the Special Manifolds