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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 | |