An introduction to multivariate statistical analysis:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Hoboken, NJ [u.a.]
Wiley-Interscience
2003
|
| Edition: | 3. ed. |
| Series: | Wiley series in probability and mathematical statistics
|
| Subjects: | |
| Online Access: | Table of contents Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XX, 721 S. graph. Darst. |
| ISBN: | 0471360910 9780471360919 |
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| adam_text | Titel: An introduction to multivariate statistical analysis
Autor: Anderson, Theodore W
Jahr: 2003
An Introduction to
Multivariate Statistical Analysis
Third Edition
T. W. ANDERSON
Stanford University
Department of Statistics
Stanford, CA
WILEY-
INTERSCIENCE
A JOHN WILEY SONS, INC., PUBLICATION
Contents
Preface to the Third Edition
Preface to the Second Edition
Preface to the First Edition
1 Introduction
1.1. Multivariate Statistical Analysis, 1
1.2. The Multivariate Normal Distribution, 3
2 The Multivariate Normal Distribution
2.1. Introduction, 6
2.2. Notions of Multivariate Distributions, 7
2.3. The Multivariate Normal Distribution, 13
2.4. The Distribution of Linear Combinations of Normally
Distributed Variates; Independence of Variates;
Marginal Distributions, 23
2.5. Conditional Distributions and Multiple Correlation
Coefficient, 33
2.6. The Characteristic Function; Moments, 41
2.7. Elliptically Contoured Distributions, 47
Problems, 56
3 Estimation of the Mean Vector and the Covariance Matrix
3.1. Introduction, 66
viii CONTENTS
3.2. The Maximum Likelihood Estimators of the Mean Vector
and the Covariance Matrix, 67
3.3. The Distribution of the Sample Mean Vector; Inference
Concerning the Mean When the Covariance Matrix Is
Known, 74
3.4. Theoretical Properties of Estimators of the Mean
Vector, 83
3.5. Improved Estimation of the Mean, 91
3.6. Elliptically Contoured Distributions, 101
Problems, 108
4 The Distributions and Uses of Sample Correlation Coefficients 115
4.1. Introduction, 115
4.2. Correlation Coefficient of a Bivariate Sample, 116
4.3. Partial Correlation Coefficients; Conditional
Distributions, 136
4.4. The Multiple Correlation Coefficient, 144
4.5. Elliptically Contoured Distributions, 158
Problems, 163
5 The Generalized T2
-Statistic 170
5.1. Introduction, 170
5.2. Derivation of the Generalized T2
-Statistic and Its
Distribution, 171
5.3. Uses of the T2
-Statistic, 177
5.4. The Distribution of T2
under Alternative Hypotheses;
The Power Function, 185
5.5. The Two-Sample Problem with Unequal Covariance
Matrices, 187
5.6. Some Optimal Properties of the T2
-Test, 190
5.7. Elliptically Contoured Distributions, 199
Problems, 201
6 Classification of Observations 207
6.1. The Problem of Classification, 207
6.2. Standards of Good Classification, 208
6.3. Procedures of Classification into One of Two Populations
with Known Probability Distributions, 211
CONTENTS ix
6.4. Classification into One of Two Known Multivariate Normal
Populations, 215
6.5. Classification into One of Two Multivariate Normal
Populations When the Parameters Are Estimated, 219
6.6. Probabilities of Misclassification, 227
6.7. Classification into One of Several Populations, 233
6.8. Classification into One of Several Multivariate Normal
Populations, 237
6.9. An Example of Classification into One of Several
Multivariate Normal Populations, 240
6.10. Classification into One of Two Known Multivariate Normal
Populations with Unequal Covariance Matrices, 242
Problems, 248
7 The Distribution of the Sample Covariance Matrix and the
Sample Generalized Variance 251
7.1. Introduction, 251
7.2. The Wishart Distribution, 252
7.3. Some Properties of the Wishart Distribution, 258
7.4. Cochran s Theorem, 262
7.5. The Generalized Variance, 264
7.6. Distribution of the Set of Correlation Coefficients When
the Population Covariance Matrix Is Diagonal, 270
7.7. The Inverted Wishart Distribution and Bayes Estimation of
the Covariance Matrix, 272
7.8. Improved Estimation of the Covariance Matrix, 276
7.9. Elliptically Contoured Distributions, 282
Problems, 285
8 Testing the General Linear Hypothesis; Multivariate Analysis
of Variance 291
8.1. Introduction, 291
8.2. Estimators of Parameters in Multivariate Linear
Regression, 292
8.3. Likelihood Ratio Criteria for Testing Linear Hypotheses
about Regression Coefficients, 298
8.4. The Distribution of the Likelihood Ratio Criterion When
the Hypothesis Is True, 304
X CONTENTS
8.5. An Asymptotic Expansion of the Distribution of the
Likelihood Ratio Criterion, 316
8.6. Other Criteria for Testing the Linear Hypothesis, 326
8.7. Tests of Hypotheses about Matrices of Regression
Coefficients and Confidence Regions, 337
8.8. Testing Equality of Means of Several Normal Distributions
with Common Covariance Matrix, 342
8.9. Multivariate Analysis of Variance, 346
8.10. Some Optimal Properties of Tests, 353
8.11. Elliptically Contoured Distributions, 370
Problems, 374
9 Testing Independence of Sets of Variates 381
9.1. Introductiom, 381
9.2. The Likelihood Ratio Criterion for Testing Independence
of Sets of Variates, 381
9.3. The Distribution of the Likelihood Ratio Criterion When
the Null Hypothesis Is True, 386
9.4. An Asymptotic Expansion of the Distribution of the
Likelihood Ratio Criterion, 390
9.5. Other Criteria, 391
9.6. Step-Down Procedures, 393
9.7. An Example, 396
9.8. The Case of Two Sets of Variates, 397
9.9. Admissibility of the Likelihood Ratio Test, 401
9.10. Monotonicity of Power Functions of Tests of
Independence of Sets, 402
9.11. Elliptically Contoured Distributions, 404
Problems, 408
10 Testing Hypotheses of Equality of Covariance Matrices and
Equality of Mean Vectors and Covariance Matrices 411
10.1. Introduction, 411
10.2. Criteria for Testing Equality of Several Covariance
Matrices, 412
10.3. Criteria for Testing That Several Normal Distributions
Are Identical, 415
10.4. Distributions of the Criteria, 417
CONTENTS
10.5. Asymptotic Expansions of the Distributions of the
Criteria, 424
10.6. The Case of Two Populations, 427
10.7. Testing the Hypothesis That a Covariance Matrix
Is Proportional to a Given Matrrix; The Sphericity
Test, 431
10.8. Testing the Hypothesis That a Covariance Matrix Is
Equal to a Given Matrix, 438
10.9. Testing the Hypothesis That a Mean Vector and a
Covariance Matrix Are Equal to a Given Vector and
Matrix, 444
10.10. Admissibility of Tests, 446
10.11. Elhptically Contoured Distributions, 449
Problems, 454
11 Principal Components 459
11.1. Introduction, 459
11.2. Definition of Principal Components in the
Population, 460
11.3. Maximum Likelihood Estimators of the Principal
Components and Their Variances, 467
11.4. Computation of the Maximum Likelihood Estimates of
the Principal Components, 469
11.5. AnExample, 471
11.6. Statistical Inference, 473
11.7. Testing Hypotheses about the Characteristic Roots of a
Covariance Matrix, 478
11.8. Elhptically Contoured Distributions, 482
Problems, 483
12 Canonical Correlations and Canonical Variables 487
12.1. Introduction, 487
12.2. Canonical Correlations and Variates in the
Population, 488
12.3. Estimation of Canonical Correlations and Variates, 498
12.4. Statistical Inference, 503
12.5. An Example, 505
12.6. Linearly Related Expected Values, 508
xii CONTENTS
12.7. Reduced Rank Regression, 514
12.8. Simultaneous Equations Models, 515
Problems, 526
13 The Distributions of Characteristic Roots and Vectors 528
13.1. Introduction, 528
13.2. The Case of Two Wishart Matrices, 529
13.3. The Case of One Nonsingular Wishart Matrix, 538
13.4. Canonical Correlations, 543
13.5. Asymptotic Distributions in the Case of One Wishart
Matrix, 545
13.6. Asymptotic Distributions in the Case of Two Wishart
Matrices, 549
13.7. Asymptotic Distribution in a Regression Model, 555
13.8. Elliptically Contoured Distributions, 563
Problems, 567
14 Factor Analysis 569
14.1. Introduction, 569
14.2. The Model, 570
14.3. Maximum Likelihood Estimators for Random
Orthogonal Factors, 576
14.4. Estimation for Fixed Factors, 586
14.5. Factor Interpretation and Transformation, 587
14.6. Estimation for Identification by Specified Zeros, 590
14.7. Estimation of Factor Scores, 591
Problems, 593
15 Patterns of Dependence; Graphical Models 595
15.1. Introduction, 595
15.2. Undirected Graphs, 596
15.3. Directed Graphs, 604
15.4. Chain Graphs, 610
15.5. Statistical Inference, 613
Appendix A Matrix Theory 624
A.l. Definition of a Matrix and Operations on Matrices, 624
A.2. Characteristic Roots and Vectors, 631
CONTENTS xiii
A.3. Partitioned Vectors and Matrices, 635
A.4. Some Miscellaneous Results, 639
A.5. Gram-Schmidt Orthogonalization and the Solution of
Linear Equations, 647
Appendix B Tables 651
B.l. Wilks Likelihood Criterion: Factors C(p, m, M) to
Adjust to Xp,m where M = n--p + l, 651
B.2. Tables of Significance Points for the Lawley-Hotelling
Trace Test, 657
B.3. Tables of Significance Points for the
Bartlett-Nanda-Pillai Trace Test, 673
B.4. Tables of Significance Points for the Roy Maximum Root
Test, 677
B.5. Significance Points for the Modified Likelihood Ratio
Test of Equality of Covariance Matrices Based on Equal
Sample Sizes, 681
B.6. Correction Factors for Significance Points for the
Sphericity Test, 683
B.7. Significance Points for the Modified Likelihood Ratio
Test 2 = 2 0 , 685
References 687
Index 713
|
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| spelling | Anderson, Theodore W. 1918-2016 Verfasser (DE-588)119091178 aut An introduction to multivariate statistical analysis T. W. Anderson 3. ed. Hoboken, NJ [u.a.] Wiley-Interscience 2003 XX, 721 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and mathematical statistics Includes bibliographical references and index Analyse multivariée Multivariate analyse gtt Statistiek gtt Statistik Multivariate Analysis Multivariate analysis Statistische Analyse (DE-588)4116599-8 gnd rswk-swf Multivariate Analyse (DE-588)4040708-1 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Statistische Analyse (DE-588)4116599-8 s DE-604 Multivariate Analyse (DE-588)4040708-1 s http://www.loc.gov/catdir/toc/wiley031/2002034317.html Table of contents HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010011791&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Anderson, Theodore W. 1918-2016 An introduction to multivariate statistical analysis Analyse multivariée Multivariate analyse gtt Statistiek gtt Statistik Multivariate Analysis Multivariate analysis Statistische Analyse (DE-588)4116599-8 gnd Multivariate Analyse (DE-588)4040708-1 gnd |
| subject_GND | (DE-588)4116599-8 (DE-588)4040708-1 (DE-588)4151278-9 |
| title | An introduction to multivariate statistical analysis |
| title_auth | An introduction to multivariate statistical analysis |
| title_exact_search | An introduction to multivariate statistical analysis |
| title_full | An introduction to multivariate statistical analysis T. W. Anderson |
| title_fullStr | An introduction to multivariate statistical analysis T. W. Anderson |
| title_full_unstemmed | An introduction to multivariate statistical analysis T. W. Anderson |
| title_short | An introduction to multivariate statistical analysis |
| title_sort | an introduction to multivariate statistical analysis |
| topic | Analyse multivariée Multivariate analyse gtt Statistiek gtt Statistik Multivariate Analysis Multivariate analysis Statistische Analyse (DE-588)4116599-8 gnd Multivariate Analyse (DE-588)4040708-1 gnd |
| topic_facet | Analyse multivariée Multivariate analyse Statistiek Statistik Multivariate Analysis Multivariate analysis Statistische Analyse Multivariate Analyse Einführung |
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