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Preface to the Third Edition | |

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Preface to the Second Edition | |

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Preface to the First Edition | |

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Introduction | |

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Multivariate Statistical Analysis | |

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The Multivariate Normal Distribution | |

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The Multivariate Normal Distribution | |

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Introduction | |

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Notions of Multivariate Distributions | |

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The Multivariate Normal Distribution | |

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The Distribution of Linear Combinations of Normally Distributed Variates; Independence of Variates; Marginal Distributions | |

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Conditional Distributions and Multiple Correlation Coefficient | |

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The Characteristic Function; Moments | |

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Elliptically Contoured Distributions | |

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Problems | |

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Estimation of the Mean Vector and the Covariance Matrix | |

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Introduction | |

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The Maximum Likelihood Estimators of the Mean Vector and the Covariance Matrix | |

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The Distribution of the Sample Mean Vector; Inference Concerning the Mean When the Covariance Matrix Is Known | |

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Theoretical Properties of Estimators of the Mean Vector | |

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Improved Estimation of the Mean | |

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Elliptically Contoured Distributions | |

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Problems | |

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The Distributions and Uses of Sample Correlation Coefficients | |

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Introduction | |

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Correlation Coefficient of a Bivariate Sample | |

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Partial Correlation Coefficients; Conditional Distributions | |

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The Multiple Correlation Coefficient | |

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Elliptically Contoured Distributions | |

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Problems | |

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The Generalized T[superscript 2]-Statistic | |

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Introduction | |

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Derivation of the Generalized T[superscript 2]-Statistic and Its Distribution | |

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Uses of the T[superscript 2]-Statistic | |

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The Distribution of T[superscript 2] under Alternative Hypotheses; The Power Function | |

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The Two-Sample Problem with Unequal Covariance Matrices | |

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Some Optimal Properties of the T[superscript 2]-Test | |

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Elliptically Contoured Distributions | |

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Problems | |

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Classification of Observations | |

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The Problem of Classification | |

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Standards of Good Classification | |

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Procedures of Classification into One of Two Populations with Known Probability Distributions | |

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Classification into One of Two Known Multivariate Normal Populations | |

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Classification into One of Two Multivariate Normal Populations When the Parameters Are Estimated | |

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Probabilities of Misclassification | |

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Classification into One of Several Populations | |

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Classification into One of Several Multivariate Normal Populations | |

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An Example of Classification into One of Several Multivariate Normal Populations | |

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Classification into One of Two Known Multivariate Normal Populations with Unequal Covariance Matrices | |

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Problems | |

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The Distribution of the Sample Covariance Matrix and the Sample Generalized Variance | |

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Introduction | |

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The Wishart Distribution | |

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Some Properties of the Wishart Distribution | |

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Cochran's Theorem | |

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The Generalized Variance | |

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Distribution of the Set of Correlation Coefficients When the Population Covariance Matrix Is Diagonal | |

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The Inverted Wishart Distribution and Bayes Estimation of the Covariance Matrix | |

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Improved Estimation of the Covariance Matrix | |

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Elliptically Contoured Distributions | |

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Problems | |

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Testing the General Linear Hypothesis; Multivariate Analysis of Variance | |

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Introduction | |

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Estimators of Parameters in Multivariate Linear Regression | |

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Likelihood Ratio Criteria for Testing Linear Hypotheses about Regression Coefficients | |

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The Distribution of the Likelihood Ratio Criterion When the Hypothesis Is True | |

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An Asymptotic Expansion of the Distribution of the Likelihood Ratio Criterion | |

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Other Criteria for Testing the Linear Hypothesis | |

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Tests of Hypotheses about Matrices of Regression Coefficients and Confidence Regions | |

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Testing Equality of Means of Several Normal Distributions with Common Covariance Matrix | |

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Multivariate Analysis of Variance | |

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Some Optimal Properties of Tests | |

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Elliptically Contoured Distributions | |

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Problems | |

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Testing Independence of Sets of Variates | |

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Introduction | |

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The Likelihood Ratio Criterion for Testing Independence of Sets of Variates | |

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The Distribution of the Likelihood Ratio Criterion When the Null Hypothesis Is True | |

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An Asymptotic Expansion of the Distribution of the Likelihood Ratio Criterion | |

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Other Criteria | |

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Step-Down Procedures | |

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An Example | |

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The Case of Two Sets of Variates | |

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Admissibility of the Likelihood Ratio Test | |

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Monotonicity of Power Functions of Tests of Independence of Sets | |

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Elliptically Contoured Distributions | |

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Problems | |

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Testing Hypotheses of Equality of Covariance Matrices and Equality of Mean Vectors and Covariance Matrices | |

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Introduction | |

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Criteria for Testing Equality of Several Covariance Matrices | |

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Criteria for Testing That Several Normal Distributions Are Identical | |

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Distributions of the Criteria | |

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Asymptotic Expansions of the Distributions of the Criteria | |

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The Case of Two Populations | |

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Testing the Hypothesis That a Covariance Matrix Is Proportional to a Given Matrrix; The Sphericity Test | |

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Testing the Hypothesis That a Covariance Matrix Is Equal to a Given Matrix | |

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Testing the Hypothesis That a Mean Vector and a Covariance Matrix Are Equal to a Given Vector and Matrix | |

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Admissibility of Tests | |

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Elliptically Contoured Distributions | |

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Problems | |

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Principal Components | |

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Introduction | |

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Definition of Principal Components in the Population | |

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Maximum Likelihood Estimators of the Principal Components and Their Variances | |

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Computation of the Maximum Likelihood Estimates of the Principal Components | |

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An Example | |

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Statistical Inference | |

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Testing Hypotheses about the Characteristic Roots of a Covariance Matrix | |

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Elliptically Contoured Distributions | |

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Problems | |

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Canonical Correlations and Canonical Variables | |

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Introduction | |

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Canonical Correlations and Variates in the Population | |

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Estimation of Canonical Correlations and Variates | |

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Statistical Inference | |

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An Example | |

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Linearly Related Expected Values | |

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Reduced Rank Regression | |

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Simultaneous Equations Models | |

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Problems | |

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The Distributions of Characteristic Roots and Vectors | |

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Introduction | |

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The Case of Two Wishart Matrices | |

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The Case of One Nonsingular Wishart Matrix | |

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Canonical Correlations | |

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Asymptotic Distributions in the Case of One Wishart Matrix | |

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Asymptotic Distributions in the Case of Two Wishart Matrices | |

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Asymptotic Distribution in a Regression Model | |

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Elliptically Contoured Distributions | |

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Problems | |

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Factor Analysis | |

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Introduction | |

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The Model | |

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Maximum Likelihood Estimators for Random Orthogonal Factors | |

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Estimation for Fixed Factors | |

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Factor Interpretation and Transformation | |

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Estimation for Identification by Specified Zeros | |

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Estimation of Factor Scores | |

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Problems | |

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Patterns of Dependence; Graphical Models | |

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Introduction | |

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Undirected Graphs | |

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Directed Graphs | |

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Chain Graphs | |

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Statistical Inference | |

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Matrix Theory | |

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Definition of a Matrix and Operations on Matrices | |

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Characteristic Roots and Vectors | |

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Partitioned Vectors and Matrices | |

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Some Miscellaneous Results | |

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Gram-Schmidt Orthogonalization and the Solution of Linear Equations | |

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Tables | |

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Wilks' Likelihood Criterion: Factors C(p, m, M) to Adjust to x[superscript 2 subscript p, m], where M = n - p + 1 | |

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Tables of Significance Points for the Lawley-Hotelling Trace Test | |

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Tables of Significance Points for the Bartlett-Nanda-Pillai Trace Test | |

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Tables of Significance Points for the Roy Maximum Root Test | |

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Significance Points for the Modified Likelihood Ratio Test of Equality of Covariance Matrices Based on Equal Sample Sizes | |

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Correction Factors for Significance Points for the Sphericity Test | |

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Significance Points for the Modified Likelihood Ratio Test [Sigma] = [Sigma subscript 0] | |

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References | |

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Index | |