Eaton Morris L. Multivariate Statistical Analysis. A Vector Space Approach

Beachwood, Ohio: Institute of Mathematical Statistics, 2007. — 519 p. — (Institute of Mathematical Statistics. Lecture Notes–Monograph Series 53). — ISBN: 9780940600690.The purpose of this book is to present a version of multivariate statistical theory in which vector space and invariance methods replace, to a large extent, more traditional multivariate methods. The book is a text. Over the past ten years, various versions have been used for graduate multivariate courses at the University of Chicago, the University of Copenhagen, and the University of Minnesota. Designed for a one year lecture course or for independent study, the book contains a full complement of problems and problem solutions.Vector Spaces Theory
Vector Spaces
Linear Transformations
Inner Product Spaces
The Cauchy–Schwarz Inequality
The Space L(V,W)
Determinants and Eigenvalues
The Spectral Theorem
Problems
Notes and References
Random Vectors
Random Vectors
Independence of Random Vectors
Special Covariance Structures
Problems
Notes and References
The Normal Distribution on A Vector Spaces
The Normal Distribution
Quadratic Forms
Independence of Quadratic Forms
Conditional Distributions
The Density of the Normal Distribution
Problems
Notes and References
Linear Statistical Models
The Classical Linear Model
More About the Gauss–Markov Theorem
Generalized Linear Models
Problems
Notes and References
Matrix Factorizations and Jacobians
Matrix Factorizations
Jacobians
Problems
Notes and References
Topological Groups and Invariant Measures
Groups
Invariant Measures and Integrals
Invariant Measures on Quotient Spaces
Transformations and Factorizations of Measures
Problems
Notes and References
First Applications of Invariance
Left O_n Invariant Distributions on n × p Matrices
Groups Acting on Sets
Invariant Probability Models
The Invariance of Likelihood Methods
Distribution Theory and Invariance
Independence and Invariance
Problems
Notes and References
The Wishart Distribution
Basic Properties
Partitioning a Wishart Matrix
The Noncentral Wishart Distribution
Distributions Related to Likelihood Ratio Tests
Problems
Notes and References
Inferernce for Means in Multivariate Linear Models
The MANOVA Model
MANOVA Problems with Block Diagonal Covariance Structure
Intraclass Covariance Structure
Symmetry Models: An Example
Complex Covariance Structures
Additional Examples of Linear Models
Problems
Notes and References
Canonical Correlation Coefficients
Population Canonical Correlation Coefficients
Sample Canonical Correlations
Some Distribution Theory
Testing for Independence
Multivariate Regression
Problems
Notes and References
Appendix
Comments on Selected Problems