A First Course in Multivariate Statistics

This graduate textbook will serve as a reference in multivariate analysis for students and researchers from a large number of areas. The book integrates statistical theory and practice, and includes the analysis of several large real-data sets.

Begins at the elementary level, presenting the first principles of multivariate distributions Includes cutting-edge topics such as the EM algorithm and principal component analysis Examples from biology, anthropology, chemistry, and other areas are worked out in detail The book contains a wealth of exercises, ranging from easy to advanced Extremely thorough coverage of the topic Includes supplementary material: sn.pub/extras

Zusammenfassung
Two chapters on discrimination and classification, including logistic regression, form the core of the book, followed by methods of testing hypotheses developed from heuristic principles, likelihood ratio tests and permutation tests.

Inhalt

1. Why Multivariate Statistics?.- 2. Joint Distribution of Several Random Variables.- 3. The Multivariate Normal Distribution.- 4. Parameter Estimation.- 5. Discrimination and Classification, Round 1.- 6. Statistical Inference for Means.- 7. Discrimination and Classification, Round 2.- 8. Linear Principal Component Analysis.- 9. Normal Mixtures.- Appendix: Selected Results From Matrix Algebra.- A.0. Preliminaries.- A.1. Partitioned Matrices.- A.2. Positive Definite Matrices.- A.3. The Cholesky Decomposition.- A.4. Vector and Matrix Differentiation.- A.5. Eigenvectors and Eigenvalues.- A.6. Spectral Decomposition of Symmetric Matrices.- A.7. The Square Root of a Positive Definite Symmetric Matrix.- A.8. Orthogonal Projections on Lines and Planes.- A.9. Simultaneous Decomposition of Two Symmetric Matrices.