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

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.