Multivariate Statistical Analysis in the Real and Complex Domains - Mathai, Arak M.; Provost, Serge B.; Haubold, Hans J.; SpringerLink (Online service) (Cham : Springer International Publishing : Imprint: Springer, 2022)
This book explores topics in multivariate statistical analysis, relevant in the real and complex domains. It utilizes simplified and unified notations to render the complex subject matter both accessible and enjoyable, drawing from clear exposition and numerous illustrative examples. The book features an in-depth treatment of theory with a fair balance of applied coverage, and a classroom lecture style so that the learning process feels organic. It also contains original results, with the goal of driving research conversations forward. This will be particularly useful for researchers working in machine learning, biomedical signal processing, and other fields that increasingly rely on complex random variables to model complex-valued data. It can also be used in advanced courses on multivariate analysis. Numerous exercises are included throughout.
1. Mathematical Preliminaries -- 2. The Univariate Gaussian and Related Distribution -- 3. Multivariate Gaussian and Related Distributions -- 4. The Matrix-variate Gaussian Distribution -- 5. Matrix-variate Gamma and Beta Distributions -- 6. Hypothesis Testing and Null Distributions -- 7. Rectangular Matrix-variate Distributions -- 8. Distributions of Eigenvalues and Eigenvectors -- 9. Principal Component Analysis -- 10. Canonical Correlation Analysis -- 11. Factor Analysis -- 12. Classification Problems -- 13. Multivariate Analysis of Variance (MANOVA) -- 14. Profile Analysis and Growth Curves -- 15. Cluster Analysis and Correspondence Analysis.
Keywords: Mathematical statistics; Statistics; Multivariate analysis; System theory; Mathematical Statistics; Statistical Theory and Methods; Multivariate Analysis; Complex Systems