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Introduction to Multivariate Statistical Analysis

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ISBN-10: 0471889873

ISBN-13: 9780471889878

Edition: 2nd 1984

Authors: Theodore W. Anderson

List price: $162.00
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Book details

List price: $162.00
Edition: 2nd
Copyright year: 1984
Publisher: John Wiley & Sons, Incorporated
Publication date: 9/28/1984
Binding: Hardcover
Pages: 704
Size: 6.36" wide x 9.63" long x 1.45" tall
Weight: 2.970
Language: English

Preface to the Third Edition
Preface to the Second Edition
Preface to the First Edition
Introduction
Multivariate Statistical Analysis
The Multivariate Normal Distribution
The Multivariate Normal Distribution
Introduction
Notions of Multivariate Distributions
The Multivariate Normal Distribution
The Distribution of Linear Combinations of Normally Distributed Variates; Independence of Variates; Marginal Distributions
Conditional Distributions and Multiple Correlation Coefficient
The Characteristic Function; Moments
Elliptically Contoured Distributions
Problems
Estimation of the Mean Vector and the Covariance Matrix
Introduction
The Maximum Likelihood Estimators of the Mean Vector and the Covariance Matrix
The Distribution of the Sample Mean Vector; Inference Concerning the Mean When the Covariance Matrix Is Known
Theoretical Properties of Estimators of the Mean Vector
Improved Estimation of the Mean
Elliptically Contoured Distributions
Problems
The Distributions and Uses of Sample Correlation Coefficients
Introduction
Correlation Coefficient of a Bivariate Sample
Partial Correlation Coefficients; Conditional Distributions
The Multiple Correlation Coefficient
Elliptically Contoured Distributions
Problems
The Generalized T[superscript 2]-Statistic
Introduction
Derivation of the Generalized T[superscript 2]-Statistic and Its Distribution
Uses of the T[superscript 2]-Statistic
The Distribution of T[superscript 2] under Alternative Hypotheses; The Power Function
The Two-Sample Problem with Unequal Covariance Matrices
Some Optimal Properties of the T[superscript 2]-Test
Elliptically Contoured Distributions
Problems
Classification of Observations
The Problem of Classification
Standards of Good Classification
Procedures of Classification into One of Two Populations with Known Probability Distributions
Classification into One of Two Known Multivariate Normal Populations
Classification into One of Two Multivariate Normal Populations When the Parameters Are Estimated
Probabilities of Misclassification
Classification into One of Several Populations
Classification into One of Several Multivariate Normal Populations
An Example of Classification into One of Several Multivariate Normal Populations
Classification into One of Two Known Multivariate Normal Populations with Unequal Covariance Matrices
Problems
The Distribution of the Sample Covariance Matrix and the Sample Generalized Variance
Introduction
The Wishart Distribution
Some Properties of the Wishart Distribution
Cochran's Theorem
The Generalized Variance
Distribution of the Set of Correlation Coefficients When the Population Covariance Matrix Is Diagonal
The Inverted Wishart Distribution and Bayes Estimation of the Covariance Matrix
Improved Estimation of the Covariance Matrix
Elliptically Contoured Distributions
Problems
Testing the General Linear Hypothesis; Multivariate Analysis of Variance
Introduction
Estimators of Parameters in Multivariate Linear Regression
Likelihood Ratio Criteria for Testing Linear Hypotheses about Regression Coefficients
The Distribution of the Likelihood Ratio Criterion When the Hypothesis Is True
An Asymptotic Expansion of the Distribution of the Likelihood Ratio Criterion
Other Criteria for Testing the Linear Hypothesis
Tests of Hypotheses about Matrices of Regression Coefficients and Confidence Regions
Testing Equality of Means of Several Normal Distributions with Common Covariance Matrix
Multivariate Analysis of Variance
Some Optimal Properties of Tests
Elliptically Contoured Distributions
Problems
Testing Independence of Sets of Variates
Introduction
The Likelihood Ratio Criterion for Testing Independence of Sets of Variates
The Distribution of the Likelihood Ratio Criterion When the Null Hypothesis Is True
An Asymptotic Expansion of the Distribution of the Likelihood Ratio Criterion
Other Criteria
Step-Down Procedures
An Example
The Case of Two Sets of Variates
Admissibility of the Likelihood Ratio Test
Monotonicity of Power Functions of Tests of Independence of Sets
Elliptically Contoured Distributions
Problems
Testing Hypotheses of Equality of Covariance Matrices and Equality of Mean Vectors and Covariance Matrices
Introduction
Criteria for Testing Equality of Several Covariance Matrices
Criteria for Testing That Several Normal Distributions Are Identical
Distributions of the Criteria
Asymptotic Expansions of the Distributions of the Criteria
The Case of Two Populations
Testing the Hypothesis That a Covariance Matrix Is Proportional to a Given Matrrix; The Sphericity Test
Testing the Hypothesis That a Covariance Matrix Is Equal to a Given Matrix
Testing the Hypothesis That a Mean Vector and a Covariance Matrix Are Equal to a Given Vector and Matrix
Admissibility of Tests
Elliptically Contoured Distributions
Problems
Principal Components
Introduction
Definition of Principal Components in the Population
Maximum Likelihood Estimators of the Principal Components and Their Variances
Computation of the Maximum Likelihood Estimates of the Principal Components
An Example
Statistical Inference
Testing Hypotheses about the Characteristic Roots of a Covariance Matrix
Elliptically Contoured Distributions
Problems
Canonical Correlations and Canonical Variables
Introduction
Canonical Correlations and Variates in the Population
Estimation of Canonical Correlations and Variates
Statistical Inference
An Example
Linearly Related Expected Values
Reduced Rank Regression
Simultaneous Equations Models
Problems
The Distributions of Characteristic Roots and Vectors
Introduction
The Case of Two Wishart Matrices
The Case of One Nonsingular Wishart Matrix
Canonical Correlations
Asymptotic Distributions in the Case of One Wishart Matrix
Asymptotic Distributions in the Case of Two Wishart Matrices
Asymptotic Distribution in a Regression Model
Elliptically Contoured Distributions
Problems
Factor Analysis
Introduction
The Model
Maximum Likelihood Estimators for Random Orthogonal Factors
Estimation for Fixed Factors
Factor Interpretation and Transformation
Estimation for Identification by Specified Zeros
Estimation of Factor Scores
Problems
Patterns of Dependence; Graphical Models
Introduction
Undirected Graphs
Directed Graphs
Chain Graphs
Statistical Inference
Matrix Theory
Definition of a Matrix and Operations on Matrices
Characteristic Roots and Vectors
Partitioned Vectors and Matrices
Some Miscellaneous Results
Gram-Schmidt Orthogonalization and the Solution of Linear Equations
Tables
Wilks' Likelihood Criterion: Factors C(p, m, M) to Adjust to x[superscript 2 subscript p, m], where M = n - p + 1
Tables of Significance Points for the Lawley-Hotelling Trace Test
Tables of Significance Points for the Bartlett-Nanda-Pillai Trace Test
Tables of Significance Points for the Roy Maximum Root Test
Significance Points for the Modified Likelihood Ratio Test of Equality of Covariance Matrices Based on Equal Sample Sizes
Correction Factors for Significance Points for the Sphericity Test
Significance Points for the Modified Likelihood Ratio Test [Sigma] = [Sigma subscript 0]
References
Index