Preface to the Third Edition | p. xv |
Preface to the Second Edition | p. xvii |
Preface to the First Edition | p. xix |
Introduction | p. 1 |
Multivariate Statistical Analysis | p. 1 |
The Multivariate Normal Distribution | p. 3 |
The Multivariate Normal Distribution | p. 6 |
Introduction | p. 6 |
Notions of Multivariate Distributions | p. 7 |
The Multivariate Normal Distribution | p. 13 |
The Distribution of Linear Combinations of Normally Distributed Variates; Independence of Variates; Marginal Distributions | p. 23 |
Conditional Distributions and Multiple Correlation Coefficient | p. 33 |
The Characteristic Function; Moments | p. 41 |
Elliptically Contoured Distributions | p. 47 |
Problems | p. 56 |
Estimation of the Mean Vector and the Covariance Matrix | p. 66 |
Introduction | p. 66 |
The Maximum Likelihood Estimators of the Mean Vector and the Covariance Matrix | p. 67 |
The Distribution of the Sample Mean Vector; Inference Concerning the Mean When the Covariance Matrix Is Known | p. 74 |
Theoretical Properties of Estimators of the Mean Vector | p. 83 |
Improved Estimation of the Mean | p. 91 |
Elliptically Contoured Distributions | p. 101 |
Problems | p. 108 |
The Distributions and Uses of Sample Correlation Coefficients | p. 115 |
Introduction | p. 115 |
Correlation Coefficient of a Bivariate Sample | p. 116 |
Partial Correlation Coefficients; Conditional Distributions | p. 136 |
The Multiple Correlation Coefficient | p. 144 |
Elliptically Contoured Distributions | p. 158 |
Problems | p. 163 |
The Generalized T[superscript 2]-Statistic | p. 170 |
Introduction | p. 170 |
Derivation of the Generalized T[superscript 2]-Statistic and Its Distribution | p. 171 |
Uses of the T[superscript 2]-Statistic | p. 177 |
The Distribution of T[superscript 2] under Alternative Hypotheses; The Power Function | p. 185 |
The Two-Sample Problem with Unequal Covariance Matrices | p. 187 |
Some Optimal Properties of the T[superscript 2]-Test | p. 190 |
Elliptically Contoured Distributions | p. 199 |
Problems | p. 201 |
Classification of Observations | p. 207 |
The Problem of Classification | p. 207 |
Standards of Good Classification | p. 208 |
Procedures of Classification into One of Two Populations with Known Probability Distributions | p. 211 |
Classification into One of Two Known Multivariate Normal Populations | p. 215 |
Classification into One of Two Multivariate Normal Populations When the Parameters Are Estimated | p. 219 |
Probabilities of Misclassification | p. 227 |
Classification into One of Several Populations | p. 233 |
Classification into One of Several Multivariate Normal Populations | p. 237 |
An Example of Classification into One of Several Multivariate Normal Populations | p. 240 |
Classification into One of Two Known Multivariate Normal Populations with Unequal Covariance Matrices | p. 242 |
Problems | p. 248 |
The Distribution of the Sample Covariance Matrix and the Sample Generalized Variance | p. 251 |
Introduction | p. 251 |
The Wishart Distribution | p. 252 |
Some Properties of the Wishart Distribution | p. 258 |
Cochran's Theorem | p. 262 |
The Generalized Variance | p. 264 |
Distribution of the Set of Correlation Coefficients When the Population Covariance Matrix Is Diagonal | p. 270 |
The Inverted Wishart Distribution and Bayes Estimation of the Covariance Matrix | p. 272 |
Improved Estimation of the Covariance Matrix | p. 276 |
Elliptically Contoured Distributions | p. 282 |
Problems | p. 285 |
Testing the General Linear Hypothesis; Multivariate Analysis of Variance | p. 291 |
Introduction | p. 291 |
Estimators of Parameters in Multivariate Linear Regression | p. 292 |
Likelihood Ratio Criteria for Testing Linear Hypotheses about Regression Coefficients | p. 298 |
The Distribution of the Likelihood Ratio Criterion When the Hypothesis Is True | p. 304 |
An Asymptotic Expansion of the Distribution of the Likelihood Ratio Criterion | p. 316 |
Other Criteria for Testing the Linear Hypothesis | p. 326 |
Tests of Hypotheses about Matrices of Regression Coefficients and Confidence Regions | p. 337 |
Testing Equality of Means of Several Normal Distributions with Common Covariance Matrix | p. 342 |
Multivariate Analysis of Variance | p. 346 |
Some Optimal Properties of Tests | p. 353 |
Elliptically Contoured Distributions | p. 370 |
Problems | p. 374 |
Testing Independence of Sets of Variates | p. 381 |
Introduction | p. 381 |
The Likelihood Ratio Criterion for Testing Independence of Sets of Variates | p. 381 |
The Distribution of the Likelihood Ratio Criterion When the Null Hypothesis Is True | p. 386 |
An Asymptotic Expansion of the Distribution of the Likelihood Ratio Criterion | p. 390 |
Other Criteria | p. 391 |
Step-Down Procedures | p. 393 |
An Example | p. 396 |
The Case of Two Sets of Variates | p. 397 |
Admissibility of the Likelihood Ratio Test | p. 401 |
Monotonicity of Power Functions of Tests of Independence of Sets | p. 402 |
Elliptically Contoured Distributions | p. 404 |
Problems | p. 408 |
Testing Hypotheses of Equality of Covariance Matrices and Equality of Mean Vectors and Covariance Matrices | p. 411 |
Introduction | p. 411 |
Criteria for Testing Equality of Several Covariance Matrices | p. 412 |
Criteria for Testing That Several Normal Distributions Are Identical | p. 415 |
Distributions of the Criteria | p. 417 |
Asymptotic Expansions of the Distributions of the Criteria | p. 424 |
The Case of Two Populations | p. 427 |
Testing the Hypothesis That a Covariance Matrix Is Proportional to a Given Matrrix; The Sphericity Test | p. 431 |
Testing the Hypothesis That a Covariance Matrix Is Equal to a Given Matrix | p. 438 |
Testing the Hypothesis That a Mean Vector and a Covariance Matrix Are Equal to a Given Vector and Matrix | p. 444 |
Admissibility of Tests | p. 446 |
Elliptically Contoured Distributions | p. 449 |
Problems | p. 454 |
Principal Components | p. 459 |
Introduction | p. 459 |
Definition of Principal Components in the Population | p. 460 |
Maximum Likelihood Estimators of the Principal Components and Their Variances | p. 467 |
Computation of the Maximum Likelihood Estimates of the Principal Components | p. 469 |
An Example | p. 471 |
Statistical Inference | p. 473 |
Testing Hypotheses about the Characteristic Roots of a Covariance Matrix | p. 478 |
Elliptically Contoured Distributions | p. 482 |
Problems | p. 483 |
Canonical Correlations and Canonical Variables | p. 487 |
Introduction | p. 487 |
Canonical Correlations and Variates in the Population | p. 488 |
Estimation of Canonical Correlations and Variates | p. 498 |
Statistical Inference | p. 503 |
An Example | p. 505 |
Linearly Related Expected Values | p. 508 |
Reduced Rank Regression | p. 514 |
Simultaneous Equations Models | p. 515 |
Problems | p. 526 |
The Distributions of Characteristic Roots and Vectors | p. 528 |
Introduction | p. 528 |
The Case of Two Wishart Matrices | p. 529 |
The Case of One Nonsingular Wishart Matrix | p. 538 |
Canonical Correlations | p. 543 |
Asymptotic Distributions in the Case of One Wishart Matrix | p. 545 |
Asymptotic Distributions in the Case of Two Wishart Matrices | p. 549 |
Asymptotic Distribution in a Regression Model | p. 555 |
Elliptically Contoured Distributions | p. 563 |
Problems | p. 567 |
Factor Analysis | p. 569 |
Introduction | p. 569 |
The Model | p. 570 |
Maximum Likelihood Estimators for Random Orthogonal Factors | p. 576 |
Estimation for Fixed Factors | p. 586 |
Factor Interpretation and Transformation | p. 587 |
Estimation for Identification by Specified Zeros | p. 590 |
Estimation of Factor Scores | p. 591 |
Problems | p. 593 |
Patterns of Dependence; Graphical Models | p. 595 |
Introduction | p. 595 |
Undirected Graphs | p. 596 |
Directed Graphs | p. 604 |
Chain Graphs | p. 610 |
Statistical Inference | p. 613 |
Matrix Theory | p. 624 |
Definition of a Matrix and Operations on Matrices | p. 624 |
Characteristic Roots and Vectors | p. 631 |
Partitioned Vectors and Matrices | p. 635 |
Some Miscellaneous Results | p. 639 |
Gram-Schmidt Orthogonalization and the Solution of Linear Equations | p. 647 |
Tables | p. 651 |
Wilks' Likelihood Criterion: Factors C(p, m, M) to Adjust to x[superscript 2 subscript p, m], where M = n - p + 1 | p. 651 |
Tables of Significance Points for the Lawley-Hotelling Trace Test | p. 657 |
Tables of Significance Points for the Bartlett-Nanda-Pillai Trace Test | p. 673 |
Tables of Significance Points for the Roy Maximum Root Test | p. 677 |
Significance Points for the Modified Likelihood Ratio Test of Equality of Covariance Matrices Based on Equal Sample Sizes | p. 681 |
Correction Factors for Significance Points for the Sphericity Test | p. 683 |
Significance Points for the Modified Likelihood Ratio Test [Sigma] = [Sigma subscript 0] | p. 685 |
References | p. 687 |
Index | p. 713 |
Table of Contents provided by Ingram. All Rights Reserved. |