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

Material type: Book; Format: print Publisher: New Jersey : John Wiley , 2003Edition: 3rd ed.Description: 721 p. ; 24 cm.ISBN: 0-471-36091-0.
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Manuales (7 días) 02. BIBLIOTECA CAMPUS PUERTO REAL
519.237/AND/int (Browse shelf) Available BIBLIOG. RECOM. 3741078714
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#### Enhanced descriptions from Syndetics:

Perfected over three editions and more than forty years, this field- and classroom-tested reference:
* Uses the method of maximum likelihood to a large extent to ensure reasonable, and in some cases optimal procedures.
* Treats all the basic and important topics in multivariate statistics.
* Adds two new chapters, along with a number of new sections.
* Provides the most methodical, up-to-date information on MV statistics available.

Indice

Bibliografía: p. 687-711

• Preface to the Third Edition (p. xv)
• Preface to the Second Edition (p. xvii)
• Preface to the First Edition (p. xix)
• 1 Introduction (p. 1)
• 1.1. Multivariate Statistical Analysis (p. 1)
• 1.2. The Multivariate Normal Distribution (p. 3)
• 2 The Multivariate Normal Distribution (p. 6)
• 2.1. Introduction (p. 6)
• 2.2. Notions of Multivariate Distributions (p. 7)
• 2.3. The Multivariate Normal Distribution (p. 13)
• 2.4. The Distribution of Linear Combinations of Normally Distributed Variates; Independence of Variates; Marginal Distributions (p. 23)
• 2.5. Conditional Distributions and Multiple Correlation Coefficient (p. 33)
• 2.6. The Characteristic Function; Moments (p. 41)
• 2.7. Elliptically Contoured Distributions (p. 47)
• Problems (p. 56)
• 3 Estimation of the Mean Vector and the Covariance Matrix (p. 66)
• 3.1. Introduction (p. 66)
• 3.2. The Maximum Likelihood Estimators of the Mean Vector and the Covariance Matrix (p. 67)
• 3.3. The Distribution of the Sample Mean Vector; Inference Concerning the Mean When the Covariance Matrix Is Known (p. 74)
• 3.4. Theoretical Properties of Estimators of the Mean Vector (p. 83)
• 3.5. Improved Estimation of the Mean (p. 91)
• 3.6. Elliptically Contoured Distributions (p. 101)
• Problems (p. 108)
• 4 The Distributions and Uses of Sample Correlation Coefficients (p. 115)
• 4.1. Introduction (p. 115)
• 4.2. Correlation Coefficient of a Bivariate Sample (p. 116)
• 4.3. Partial Correlation Coefficients; Conditional Distributions (p. 136)
• 4.4. The Multiple Correlation Coefficient (p. 144)
• 4.5. Elliptically Contoured Distributions (p. 158)
• Problems (p. 163)
• 5 The Generalized T[superscript 2]-Statistic (p. 170)
• 5.1. Introduction (p. 170)
• 5.2. Derivation of the Generalized T[superscript 2]-Statistic and Its Distribution (p. 171)
• 5.3. Uses of the T[superscript 2]-Statistic (p. 177)
• 5.4. The Distribution of T[superscript 2] under Alternative Hypotheses; The Power Function (p. 185)
• 5.5. The Two-Sample Problem with Unequal Covariance Matrices (p. 187)
• 5.6. Some Optimal Properties of the T[superscript 2]-Test (p. 190)
• 5.7. Elliptically Contoured Distributions (p. 199)
• Problems (p. 201)
• 6 Classification of Observations (p. 207)
• 6.1. The Problem of Classification (p. 207)
• 6.2. Standards of Good Classification (p. 208)
• 6.3. Procedures of Classification into One of Two Populations with Known Probability Distributions (p. 211)
• 6.4. Classification into One of Two Known Multivariate Normal Populations (p. 215)
• 6.5. Classification into One of Two Multivariate Normal Populations When the Parameters Are Estimated (p. 219)
• 6.6. Probabilities of Misclassification (p. 227)
• 6.7. Classification into One of Several Populations (p. 233)
• 6.8. Classification into One of Several Multivariate Normal Populations (p. 237)
• 6.9. An Example of Classification into One of Several Multivariate Normal Populations (p. 240)
• 6.10. Classification into One of Two Known Multivariate Normal Populations with Unequal Covariance Matrices (p. 242)
• Problems (p. 248)
• 7 The Distribution of the Sample Covariance Matrix and the Sample Generalized Variance (p. 251)
• 7.1. Introduction (p. 251)
• 7.2. The Wishart Distribution (p. 252)
• 7.3. Some Properties of the Wishart Distribution (p. 258)
• 7.4. Cochran's Theorem (p. 262)
• 7.5. The Generalized Variance (p. 264)
• 7.6. Distribution of the Set of Correlation Coefficients When the Population Covariance Matrix Is Diagonal (p. 270)
• 7.7. The Inverted Wishart Distribution and Bayes Estimation of the Covariance Matrix (p. 272)
• 7.8. Improved Estimation of the Covariance Matrix (p. 276)
• 7.9. Elliptically Contoured Distributions (p. 282)
• Problems (p. 285)
• 8 Testing the General Linear Hypothesis; Multivariate Analysis of Variance (p. 291)
• 8.1. Introduction (p. 291)
• 8.2. Estimators of Parameters in Multivariate Linear Regression (p. 292)
• 8.3. Likelihood Ratio Criteria for Testing Linear Hypotheses about Regression Coefficients (p. 298)
• 8.4. The Distribution of the Likelihood Ratio Criterion When the Hypothesis Is True (p. 304)
• 8.5. An Asymptotic Expansion of the Distribution of the Likelihood Ratio Criterion (p. 316)
• 8.6. Other Criteria for Testing the Linear Hypothesis (p. 326)
• 8.7. Tests of Hypotheses about Matrices of Regression Coefficients and Confidence Regions (p. 337)
• 8.8. Testing Equality of Means of Several Normal Distributions with Common Covariance Matrix (p. 342)
• 8.9. Multivariate Analysis of Variance (p. 346)
• 8.10. Some Optimal Properties of Tests (p. 353)
• 8.11. Elliptically Contoured Distributions (p. 370)
• Problems (p. 374)
• 9 Testing Independence of Sets of Variates (p. 381)
• 9.1. Introduction (p. 381)
• 9.2. The Likelihood Ratio Criterion for Testing Independence of Sets of Variates (p. 381)
• 9.3. The Distribution of the Likelihood Ratio Criterion When the Null Hypothesis Is True (p. 386)
• 9.4. An Asymptotic Expansion of the Distribution of the Likelihood Ratio Criterion (p. 390)
• 9.5. Other Criteria (p. 391)
• 9.6. Step-Down Procedures (p. 393)
• 9.7. An Example (p. 396)
• 9.8. The Case of Two Sets of Variates (p. 397)
• 9.9. Admissibility of the Likelihood Ratio Test (p. 401)
• 9.10. Monotonicity of Power Functions of Tests of Independence of Sets (p. 402)
• 9.11. Elliptically Contoured Distributions (p. 404)
• Problems (p. 408)
• 10 Testing Hypotheses of Equality of Covariance Matrices and Equality of Mean Vectors and Covariance Matrices (p. 411)
• 10.1. Introduction (p. 411)
• 10.2. Criteria for Testing Equality of Several Covariance Matrices (p. 412)
• 10.3. Criteria for Testing That Several Normal Distributions Are Identical (p. 415)
• 10.4. Distributions of the Criteria (p. 417)
• 10.5. Asymptotic Expansions of the Distributions of the Criteria (p. 424)
• 10.6. The Case of Two Populations (p. 427)
• 10.7. Testing the Hypothesis That a Covariance Matrix Is Proportional to a Given Matrrix; The Sphericity Test (p. 431)
• 10.8. Testing the Hypothesis That a Covariance Matrix Is Equal to a Given Matrix (p. 438)
• 10.9. Testing the Hypothesis That a Mean Vector and a Covariance Matrix Are Equal to a Given Vector and Matrix (p. 444)
• 10.10. Admissibility of Tests (p. 446)
• 10.11. Elliptically Contoured Distributions (p. 449)
• Problems (p. 454)
• 11 Principal Components (p. 459)
• 11.1. Introduction (p. 459)
• 11.2. Definition of Principal Components in the Population (p. 460)
• 11.3. Maximum Likelihood Estimators of the Principal Components and Their Variances (p. 467)
• 11.4. Computation of the Maximum Likelihood Estimates of the Principal Components (p. 469)
• 11.5. An Example (p. 471)
• 11.6. Statistical Inference (p. 473)
• 11.7. Testing Hypotheses about the Characteristic Roots of a Covariance Matrix (p. 478)
• 11.8. Elliptically Contoured Distributions (p. 482)
• Problems (p. 483)
• 12 Canonical Correlations and Canonical Variables (p. 487)
• 12.1. Introduction (p. 487)
• 12.2. Canonical Correlations and Variates in the Population (p. 488)
• 12.3. Estimation of Canonical Correlations and Variates (p. 498)
• 12.4. Statistical Inference (p. 503)
• 12.5. An Example (p. 505)
• 12.6. Linearly Related Expected Values (p. 508)
• 12.7. Reduced Rank Regression (p. 514)
• 12.8. Simultaneous Equations Models (p. 515)
• Problems (p. 526)
• 13 The Distributions of Characteristic Roots and Vectors (p. 528)
• 13.1. Introduction (p. 528)
• 13.2. The Case of Two Wishart Matrices (p. 529)
• 13.3. The Case of One Nonsingular Wishart Matrix (p. 538)
• 13.4. Canonical Correlations (p. 543)
• 13.5. Asymptotic Distributions in the Case of One Wishart Matrix (p. 545)
• 13.6. Asymptotic Distributions in the Case of Two Wishart Matrices (p. 549)
• 13.7. Asymptotic Distribution in a Regression Model (p. 555)
• 13.8. Elliptically Contoured Distributions (p. 563)
• Problems (p. 567)
• 14 Factor Analysis (p. 569)
• 14.1. Introduction (p. 569)
• 14.2. The Model (p. 570)
• 14.3. Maximum Likelihood Estimators for Random Orthogonal Factors (p. 576)
• 14.4. Estimation for Fixed Factors (p. 586)
• 14.5. Factor Interpretation and Transformation (p. 587)
• 14.6. Estimation for Identification by Specified Zeros (p. 590)
• 14.7. Estimation of Factor Scores (p. 591)
• Problems (p. 593)
• 15 Patterns of Dependence; Graphical Models (p. 595)
• 15.1. Introduction (p. 595)
• 15.2. Undirected Graphs (p. 596)
• 15.3. Directed Graphs (p. 604)
• 15.4. Chain Graphs (p. 610)
• 15.5. Statistical Inference (p. 613)
• Appendix A Matrix Theory (p. 624)
• A.1. Definition of a Matrix and Operations on Matrices (p. 624)
• A.2. Characteristic Roots and Vectors (p. 631)
• A.3. Partitioned Vectors and Matrices (p. 635)
• A.4. Some Miscellaneous Results (p. 639)
• A.5. Gram-Schmidt Orthogonalization and the Solution of Linear Equations (p. 647)
• Appendix B Tables (p. 651)
• B.1. Wilks' Likelihood Criterion: Factors C(p, m, M) to Adjust to x[superscript 2 subscript p, m], where M = n - p + 1 (p. 651)
• B.2. Tables of Significance Points for the Lawley-Hotelling Trace Test (p. 657)
• B.3. Tables of Significance Points for the Bartlett-Nanda-Pillai Trace Test (p. 673)
• B.4. Tables of Significance Points for the Roy Maximum Root Test (p. 677)
• B.5. Significance Points for the Modified Likelihood Ratio Test of Equality of Covariance Matrices Based on Equal Sample Sizes (p. 681)
• B.6. Correction Factors for Significance Points for the Sphericity Test (p. 683)
• B.7. Significance Points for the Modified Likelihood Ratio Test [Sigma] = [Sigma subscript 0] (p. 685)
• References (p. 687)
• Index (p. 713)

### Author notes provided by Syndetics

Theodore Wilbur Anderson was born in Minneapolis, Minnesota on June 5, 1918. He received a bachelor's degree in mathematics from Northwestern University and a master's degree and a Ph.D. in mathematics from Princeton University. During World War II, he did war research work on long-range weather forecasting, gunfire strategies for battleships, and explosives testing at Princeton University. He was a statistician who helped pave the way for modern econometrics and data analysis. He wrote several books including An Introduction to Multivariate Statistical Analysis and The Statistical Analysis of Time Series. He died from heart failure on September 17, 2016 at the age of 98.

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