Multivariate statistical analysis

Author: Zhang Runchu
Publisher:
Publish Date: 2006-09-01
Features: This book systematically presents the fundamental theories of multivariate distributions in statistics and commonly used multivariate data analysis methods. The theory of multivariate distributions includes Wishart distribution, T2 distribution, Λ distribution, multivariate Beta distribution, parameter estimation and hypothesis testing for multivariate normal distributions, and parameter estimation and hypothesis testing theory for general multivariate distributions. The methods of multivariate data analysis include multivariate linear regression models, discriminant analysis, principal component analysis, factor analysis, correspondence analysis, cluster analysis, canonical correlation analysis, and multidimensional scaling. It emphasizes the theoretical systematicity of the discipline as a branch, providing necessary and concise mathematical derivations for some fundamental theorems, while also focusing on the diversity of data analysis methods. It elaborates on each method in detail, including background, use of mathematical tools, computational steps, application techniques, and the connections between various methods, including recent developments. The book provides some insightful examples and exercises. The appendix at the end offers additional algebraic supplementary knowledge. This book can serve as a textbook for senior undergraduate and graduate students in mathematics departments, departments of mathematical statistics or statistics, departments of econometrics, departments of biostatistics, and related disciplines in universities and colleges. It can also be used as a reference book for teachers or scientists and engineers in fields such as mathematics, biology, medicine, economics, finance, and engineering.