Table of Contents
DRAFT
(NOTE: Each chapter begins with an Introduction, and
concludes with Exercises and References.)
I. GETTING STARTED.
1. Aspects of Multivariate Analysis.
Applications of Multivariate Techniques. The Organization of Data.
Data Displays and Pictorial Representations. Distance. Final
Comments.
2. 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.
3. 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.
4. 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. II. INFERENCES ABOUT MULTIVARIATE MEANS AND LINEAR
MODELS.
5. 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.
6. 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 Repealed Measures, Designs, and Growth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.
7. 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. III. ANALYSIS OF A COVARIANCE STRUCTURE.
8.
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.
9. 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.
10.
Canonical Correlation Analysis
Canonical Variates and Canonical Correlations. Interpreting the
Population Canonical Variables. The Sample Canonical Variates and
Sample Canonical Correlations. Additional Sample Descriptive
Measures. Large Sample Inferences. IV. CLASSIFICATION AND GROUPING
TECHNIQUES.
11. Discrimination and Classification.
Separation and Classification for Two Populations. Classifications
with Two Multivariate Normal Populations. Evaluating Classification
Functions. Fisher's Discriminant Function...nSeparation of
Populations. Classification with Several Populations. Fisher's
Method for Discriminating among Several Populations. Final
Comments.
12. Clustering, Distance Methods and
Ordination.
Similarity Measures. Hierarchical Clustering Methods.
Nonhierarchical Clustering Methods. Multidimensional Scaling.
Correspondence Analysis. Biplots for Viewing Sample Units and
Variables. Procustes Analysis: A Method for Comparing
Configurations.
Appendix.
Standard Normal Probabilities. Student's
t-Distribution
Percentage Points. ...c2 Distribution Percentage Points.
F-Distribution Percentage Points.
F-Distribution
Percentage Points (...a = .10).
F-Distribution Percentage
Points (...a = .05).
F-Distribution Percentage Points (...a
= .01).
Data Index.
Subject Index.About the Author
Dean W. Wichern is Professor Emeritus at the Mays School of
Business at Texas A&M University. He holds membership in the
American Statistical Association, Royal Statistical Society,
International Institute of Forecasters, and Institute for
Operations Research and the Management Sciences. He is the author
for four textbooks and was Associate Editor of Journal of Business
and Economic Statistics from 1983-1991. Professor Richard A.
Johnson is Professor in the Department of Statistics at the
University of Wisconsin. He is a Fellow of the Institute of
Mathematical Statistics and the American Statistical Association
and he is amember of the Royal Statistical Society and
International Statistical Institute. He is the author of six
textbooks and over 120 technical publications and is the founding
Editor of Statistics and Probability Letters (1981-).