DRAFT (NOTE: Each chapter begins with an Introduction, and concludes with Exercises and References.)
Getting Started
Aspects of Multivariate Analysis
Applications of Multivariate Techniques
The Organization of Data
Data Displays and Pictorial Representations
Distance
Final Comments
Matrix Algebra and Random Vectors
Some Basics of Matrix and Vector Algebra
Positive Definite Matrices
A Square-Root Matrix
Random Vectors and Matrices
Mean Vectors and Covariance Matrices
Matrix Inequalities and Maximization
Supplement 2A Vectors and Matrices: Basic Concepts
Sample Geometry and Random Sampling
The Geometry of the Sample
Random Samples and the Expected Values of the Sample Mean and Covariance Matrix
Generalized Variance
Sample Mean, Covariance, and Correlation as Matrix Operations
Sample Values of Linear Combinations of Variables
The Multivariate Normal Distribution
The Multivariate Normal Density and Its Properties
Sampling from a Multivariate Normal Distribution and Maximum Likelihood Estimation
The Sampling Distribution of `X and S. Large-Sample Behavior of `X and S. Assessing the Assumption of Normality
Detecting Outliners and Data Cleaning
Transformations to Near Normality
Inferences About Multivariate Means and Linear Models
Inferences About a Mean Vector
The Plausibility of m0 as a Value for a Normal Population Mean
Hotelling's T 2 and Likelihood Ratio Tests
Confidence Regions and Simultaneous Comparisons of Component Means
Large Sample Inferences about a Population Mean Vector
Multivariate Quality Control Charts
Inferences about Mean Vectors When Some Observations Are Missing
Difficulties Due To Time Dependence in Multivariate Observations
Supplement 5A Simultaneous Confidence Intervals and Ellipses as Shadows of the p-Dimensional Ellipsoids
Comparisons of Several Multivariate Means
Paired Comparisons and a Repeated Measures Design
Comparing Mean Vectors from Two Populations
Comparison of Several Multivariate Population Means (One-Way MANOVA). Simultaneous Confidence Intervals for Treatment Effects
Two-Way Multivariate Analysis of Variance
Profile Analysis
Repealed Measures, Designs, and Growth Curves
Perspectives and a Strategy for Analyzing Multivariate Models
Multivariate Linear Regression Models
The Classical Linear Regression Model
Least Squares Estimation
Inferences About the Regression Model
Inferences from the Estimated Regression Function
Model Checking and Other Aspects of Regression
Multivariate Multiple Regression
The Concept of Linear Regression
Comparing the Two Formulations of the Regression Model
Multiple Regression Models with Time Dependant Errors
Supplement 7A The Distribution of the Likelihood Ratio for the Multivariate Regression Model
Analysis Of A Covariance Structure
Principal Components
Population Principal Components
Summarizing Sample Variation by Principal Components
Graphing the Principal Components
Large-Sample Inferences
Monitoring Quality with Principal Components
Supplement 8A The Geometry of the Sample Principal Component Approximation
Factor Analysis and Inference for Structured Covariance Matrices
The Orthogonal Factor Model
Methods of Estimation
Factor Rotation
Factor Scores
Perspectives and a Strategy for Factor Analysis
Structural Equation Models
Supplement 9A Some Computational Details for Maximum Likelihood Estimation
Canonical Correlation Analysis
Canonical Variates and Canonical Correlations
Interpreting the Population Canonical Variables
The Sample Canonical Variates and Sample Canonical Correlations
Additional Sample Descriptive Meas