An introduction to multivariate statistical analysis

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An introduction to multivariate statistical analysis / T.W. Anderson

版:: 3rd ed
資料種別:: 図書
出版情報:: Hoboken, N.J. : Wiley-Interscience, c2003
形態:: xx, 721 p. ; 25 cm
シリーズ名:: Wiley series in probability and mathematical statistics <BA00019013>
著者名:: Anderson, T. W. (Theodore Wilbur), 1918- <DA00076501>
ISBN:: 9780471360919 [0471360910] (: cloth)
書誌ID:: BA63301060

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注記:

Includes bibliographical references (p. 687-711) and index

主題:

Multivariate analysis

言語:

英語

目次情報:

Preface to the Third Edition

Preface to the Second Edition

Preface to the First Edition

Introduction / 1：

Multivariate Statistical Analysis / 1.1.：

The Multivariate Normal Distribution / 1.2.：

Notions of Multivariate Distributions / 2：

The Distribution of Linear Combinations of Normally Distributed Variates; Independence of Variates; Marginal Distributions / 2.3.：

Conditional Distributions and Multiple Correlation Coefficient / 2.5.：

The Characteristic Function; Moments / 2.6.：

Elliptically Contoured Distributions / 2.7.：

Problems

Estimation of the Mean Vector and the Covariance Matrix / 3：

The Maximum Likelihood Estimators of the Mean Vector and the Covariance Matrix / 3.1.：

The Distribution of the Sample Mean Vector; Inference Concerning the Mean When the Covariance Matrix Is Known / 3.3.：

Theoretical Properties of Estimators of the Mean Vector / 3.4.：

Improved Estimation of the Mean / 3.5.：

The Distributions and Uses of Sample Correlation Coefficients / 3.6.：

Correlation Coefficient of a Bivariate Sample / 4.1.：

Partial Correlation Coefficients; Conditional Distributions / 4.3.：

The Multiple Correlation Coefficient / 4.4.：

The Generalized T[superscript 2]-Statistic / 4.5.：

Derivation of the Generalized T[superscript 2]-Statistic and Its Distribution / 5.1.：

Uses of the T[superscript 2]-Statistic / 5.3.：

The Distribution of T[superscript 2] under Alternative Hypotheses; The Power Function / 5.4.：

The Two-Sample Problem with Unequal Covariance Matrices / 5.5.：

Some Optimal Properties of the T[superscript 2]-Test / 5.6.：

Classification of Observations / 5.7.：

The Problem of Classification / 6.1.：

Standards of Good Classification / 6.2.：

Procedures of Classification into One of Two Populations with Known Probability Distributions / 6.3.：

Classification into One of Two Known Multivariate Normal Populations / 6.4.：

Classification into One of Two Multivariate Normal Populations When the Parameters Are Estimated / 6.5.：

Probabilities of Misclassification / 6.6.：

Classification into One of Several Populations / 6.7.：

Classification into One of Several Multivariate Normal Populations / 6.8.：

An Example of Classification into One of Several Multivariate Normal Populations / 6.9.：

Classification into One of Two Known Multivariate Normal Populations with Unequal Covariance Matrices / 6.10.：

The Distribution of the Sample Covariance Matrix and the Sample Generalized Variance / 7：

The Wishart Distribution / 7.1.：

Some Properties of the Wishart Distribution / 7.3.：

Cochran's Theorem / 7.4.：

The Generalized Variance / 7.5.：

Distribution of the Set of Correlation Coefficients When the Population Covariance Matrix Is Diagonal / 7.6.：

The Inverted Wishart Distribution and Bayes Estimation of the Covariance Matrix / 7.7.：

Improved Estimation of the Covariance Matrix / 7.8.：

Testing the General Linear Hypothesis; Multivariate Analysis of Variance / 7.9.：

Estimators of Parameters in Multivariate Linear Regression / 8.1.：

Likelihood Ratio Criteria for Testing Linear Hypotheses about Regression Coefficients / 8.3.：

The Distribution of the Likelihood Ratio Criterion When the Hypothesis Is True / 8.4.：

An Asymptotic Expansion of the Distribution of the Likelihood Ratio Criterion / 8.5.：

Other Criteria for Testing the Linear Hypothesis / 8.6.：

Tests of Hypotheses about Matrices of Regression Coefficients and Confidence Regions / 8.7.：

Testing Equality of Means of Several Normal Distributions with Common Covariance Matrix / 8.8.：

Multivariate Analysis of Variance / 8.9.：

Some Optimal Properties of Tests / 8.10.：

Testing Independence of Sets of Variates / 8.11.：

The Likelihood Ratio Criterion for Testing Independence of Sets of Variates / 9.1.：

The Distribution of the Likelihood Ratio Criterion When the Null Hypothesis Is True / 9.3.：

Other Criteria / 9.4.：

Step-Down Procedures / 9.6.：

An Example / 9.7.：

The Case of Two Sets of Variates / 9.8.：

Admissibility of the Likelihood Ratio Test / 9.9.：

Monotonicity of Power Functions of Tests of Independence of Sets / 9.10.：

Testing Hypotheses of Equality of Covariance Matrices and Equality of Mean Vectors and Covariance Matrices / 9.11.：

Criteria for Testing Equality of Several Covariance Matrices / 10.1.：

Criteria for Testing That Several Normal Distributions Are Identical / 10.3.：

Distributions of the Criteria / 10.4.：

Asymptotic Expansions of the Distributions of the Criteria / 10.5.：

The Case of Two Populations / 10.6.：

Testing the Hypothesis That a Covariance Matrix Is Proportional to a Given Matrrix; The Sphericity Test / 10.7.：

Testing the Hypothesis That a Covariance Matrix Is Equal to a Given Matrix / 10.8.：

Testing the Hypothesis That a Mean Vector and a Covariance Matrix Are Equal to a Given Vector and Matrix / 10.9.：

Admissibility of Tests / 10.10.：

Principal Components / 10.11.：

Definition of Principal Components in the Population / 11.1.：

Maximum Likelihood Estimators of the Principal Components and Their Variances / 11.3.：

Computation of the Maximum Likelihood Estimates of the Principal Components / 11.4.：

Statistical Inference / 11.5.：

Testing Hypotheses about the Characteristic Roots of a Covariance Matrix / 11.7.：

Canonical Correlations and Canonical Variables / 11.8.：

Canonical Correlations and Variates in the Population / 12.1.：

Estimation of Canonical Correlations and Variates / 12.3.：

Linearly Related Expected Values / 12.4.：

Reduced Rank Regression / 12.7.：

Simultaneous Equations Models / 12.8.：

The Distributions of Characteristic Roots and Vectors / 13：

The Case of Two Wishart Matrices / 13.1.：

The Case of One Nonsingular Wishart Matrix / 13.3.：

Canonical Correlations / 13.4.：

Asymptotic Distributions in the Case of One Wishart Matrix / 13.5.：

Asymptotic Distributions in the Case of Two Wishart Matrices / 13.6.：

Asymptotic Distribution in a Regression Model / 13.7.：

Factor Analysis / 13.8.：

The Model / 14.1.：

Maximum Likelihood Estimators for Random Orthogonal Factors / 14.3.：

Estimation for Fixed Factors / 14.4.：

Factor Interpretation and Transformation / 14.5.：

Estimation for Identification by Specified Zeros / 14.6.：

Estimation of Factor Scores / 14.7.：

Patterns of Dependence; Graphical Models / 15：

Undirected Graphs / 15.1.：

Directed Graphs / 15.3.：

Chain Graphs / 15.4.：

Matrix Theory / 15.5.：

Definition of a Matrix and Operations on Matrices / A.1.：

Characteristic Roots and Vectors / A.2.：

Partitioned Vectors and Matrices / A.3.：

Some Miscellaneous Results / A.4.：

Gram-Schmidt Orthogonalization and the Solution of Linear Equations / A.5.：

Tables / Appendix B：

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

Tables of Significance Points for the Lawley-Hotelling Trace Test / B.2.：

Tables of Significance Points for the Bartlett-Nanda-Pillai Trace Test / B.3.：

Tables of Significance Points for the Roy Maximum Root Test / B.4.：

Significance Points for the Modified Likelihood Ratio Test of Equality of Covariance Matrices Based on Equal Sample Sizes / B.5.：

Correction Factors for Significance Points for the Sphericity Test / B.6.：

Significance Points for the Modified Likelihood Ratio Test [Sigma] = [Sigma subscript 0] / B.7.：

References

Index

Preface to the Third Edition

Preface to the Second Edition

Preface to the First Edition

Introduction / 1：

Multivariate Statistical Analysis / 1.1.：

The Multivariate Normal Distribution / 1.2.：

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