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