Multivariate analysis:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Amsterdam [u.a.]
Acad. Press
2003
|
| Edition: | Reprint. |
| Series: | Probability and mathematical statistics
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| Subjects: | |
| Online Access: | Publisher description Table of contents Inhaltsverzeichnis |
| Physical Description: | XV, 518 S. graph. Darst. |
| ISBN: | 0124712525 |
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Record in the Search Index
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| adam_text | Titel: Multivariate analysis
Autor: Mardia, Kanti V
Jahr: 2003
CONTENTS
Preface ..........................................................vii
Acknowledgements................................................x
Chapter 1—Introduction............................................1
1.1 Objects and variables........................................1
1.2 Some multivariate problems and techniques....................2
1.3 The data matrix ............................................8
1.4 Summary statistics ..........................................9
1.5 Linear combinations ........................................13
1.6 Geometrical ideas ..........................................16
1.7 Graphical representations....................................17
*1.8 Measures of multivariate skewness and kurtosis ................20
Exercises and complements ......................................22
Chapter 2—Basic Properties of Random Vectors......................26
2.1 Cumulative distribution functions and probability density func-
tions ......................................................26
2.2 Population moments ........................................28
2.3 Characteristic functions......................................33
2.4 Transformations............................................35
2.5 The multinormal distribution ................................36
2.6 Some multivariate generalizations of univariate distributions ... 43
2.7 Families of distributions......................................45
2.8 Random samples............................................49
2.9 Limit theorems ............................................51
Exercises and complements ......................................53
Chapter 3—Normal Distribution Theory..............................59
3.1 Characterization and properties ..............................59
3.2 Linear forms ..............................................62
3.3 Transformations of normal data matrices ......................64
3.4 The Wishart distribution ....................................66
CONTENTS xn
3.5 The Hotelling T2distribution ................ 73
3.6 Mahalanobis distance.................... 76
3.7 Statistics based on the Wishart distribution .......... 80
3.8 Other distributions related to the multinomial..................85
Exercises and complements........................................86
Chapter A—Estimation ............................................96
4.1 Likelihood and sufficiency....................................96
4.2 Maximum likelihood estimation ..............................102
4.3 Other techniques and concepts................................109
Exercises and complements ......................................113
Chapter 5—Hypothesis Testing......................................120
5.1 Introduction................................................120
5.2 The techniques introduced ..................................123
5.3 The techniques further illustrated ............................131
*5.4 The Behrens-Fisher problem ................................142
5.5 Simultaneous confidence intervals ............................144
5.6 Multivariate hypothesis testing: some general points ............147
*5.7 Non-normal data............................................148
5.8 A non-parametric test for the bivariate two-sample problem . . . 149
Exercises and complements ......................................151
Chapter 6—Multivariate Regression Analysis..........................157
6.1 Introduction................................................157
6.2 Maximum likelihood estimation ..............................158
6.3 The general linear hypothesis..................................161
6.4 Design matrices of degenerate rank............................164
6.5 Multiple correlation ........................................167
6.6 Least squares estimation......................................171
6.7 Discarding of variables ......................................175
Exercises and complements ......................................180
Chapter 7—Econometrics ..........................................185
7.1 Introduction................................................185
7.2 Instrumental variables and two-stage least squares ..............186
7.3 Simultaneous equation systems................................191
7.4 Single-equation estimators ..................................199
7.5 System estimators ..........................................203
7.6 Comparison of estimators....................................208
Exercises and complements ......................................208
Chapter 8—Principal Component Analysis............................213
8.1 Introduction................................................213
8.2 Definition and properties of principal components ..............214
8.3 Sampling properties of principal components....................229
8.4 Testing hypotheses about principal components ................233
8.5 Correspondence analysis ....................................237
8.6 Allometry—the measurement of size and shape ................239
xiii CONTENTS
8.7 Discarding of variables ......................................242
8.8 Principal component analysis in regression......................244
Exercises and complements ......................................246
Chapter 9—Factor Analysis ........................................255
9.1 Introduction................................................255
9.2 The factor model............................................256
9.3 Principal factor analysis......................................261
9.4 Maximum likelihood factor analysis............................263
9.5 Goodness of fit test..........................................267
9.6 Rotation of factors..........................................268
9.7 Factor scores ..............................................273
9.8 Relationships between factor analysis and principal component
analysis....................................................275
9.9 Analysis of covariance structures..............................276
Exercises and complements ......................................276
Chapter 10—Canonical Correlation Analysis..........................281
10.1 Introduction ..............................................281
10.2 Mathematical development..................................282
10.3 Qualitative data and dummy variables........................290
10.4 Qualitative and quantative data..............................293
Exercises and complements ......................................295
Chapter 11—Discriminant Analysis..................................300
11.1 Introduction..............................................300
11.2 Discrimination when the populations are known................301
11.3 Discrimination under estimation ............................309
11.4 Is discrimination worthwhile?................................318
11.5 Fisher s linear discriminant function..........................318
11.6 Probabilities of misclassification ............................320
11.7 Discarding of variables......................................322
11.8 When does correlation improve discrimination?................324
Exercises and complements ......................................325
Chapter 12—Multivariate Analysis of Variance........................333
12.1 Introduction ..............................................333
12.2 Formulation of multivariate one-way classification..............333
12.3 The likelihood ratio principle................................334
12.4 Testing fixed contrasts......................................337
12.5 Canonical variables and a test of dimensionality................338
12.6 The union intersection approach ............................348
12.7 Two-way classification......................................350
Exercises and complements........................................356
Chapter 13—Cluster Analysis ......................................360
13.1 Introduction................................................360
13.2 A probabilistic formulation..................................361
13.3 Hierarchical methods ......................................369
13.4 Distances and similarities ..................................375
CONTENTS Xiv
13.5 Other methods and comparative approach ....................384
Exercises and complements ......................................386
Chapter 14—Multidimensional Scaling................................394
14.1 Introduction ..............................................394
14.2 Classical solution ..........................................397
14.3 Duality between principal coordinate analysis and principal com-
ponent analysis............................................404
14.4 Optimal properties of the classical solution and goodness of fit . . 406
14.5 Seriation..................................................409
14.6 Non-metric methods........................................413
14.7 Goodness of fit measure: Procrustes rotation......................416
*14.8 Multi-sample problem and canonical variâtes..................419
Exercises and complements ......................................420
Chapter 15—Directional Data ......................................424
15.1 Introduction ..............................................424
15.2 Descriptive measures ......................................426
15.3 Basic distributions..........................................428
15.4 Distribution theory ........................................435
15.5 Maximum likelihood estimators for the von Mises-Fisher distribu-
tion ......................................................437
15.6 Test of uniformity: the Rayleigh test..........................439
15.7 Some other problems ......................................441
Exercises and complements ......................................446
Appendix A—Matrix Algebra ......................................452
A.l Introduction ..............................................452
A.2 Matrix operations..........................................455
A.3 Further particular matrices and types of matrix ................460
A.4 Vector spaces, rank, and linear equations......................462
A.5 Linear transformations......................................465
A.6 Eigenvalues and eigenvectors................................466
A.l Quadratic forms and definiteness ............................474
*A.8 Generalized inverse........................................476
A.9 Matrix differentiation and maximization problems..............478
A.10 Geometrical ideas..........................................481
Appendix B—Univariate Statistics ..................................486
B.l Introduction ..............................................486
B.2 Normal distribution........................................486
B.3 Chi-squared distribution....................................487
B.4 F and beta variables........................................487
B.5 t distribution..............................................488
Appendix C—Tables ..............................................489
Table C. 1 Upper percentage points of the xl distribution.....490
XV CONTENTS
Table C.2 Upper percentage points of the t„ distribution.......491
Table C.3 Upper percentage points of the F„1,„2 distribution.....492
Table C.4 Upper percentage points 6a of 0(p, vu v2), the largest
eigenvalue of |B - 8(W+B)| = 0 for p = 2.........494
References............................V 497
List of Main Notations and Abbreviations............... 508
Subject Index........................... 510
Author Index........................... 519
|
| adam_txt |
Titel: Multivariate analysis
Autor: Mardia, Kanti V
Jahr: 2003
CONTENTS
Preface .vii
Acknowledgements.x
Chapter 1—Introduction.1
1.1 Objects and variables.1
1.2 Some multivariate problems and techniques.2
1.3 The data matrix .8
1.4 Summary statistics .9
1.5 Linear combinations .13
1.6 Geometrical ideas .16
1.7 Graphical representations.17
*1.8 Measures of multivariate skewness and kurtosis .20
Exercises and complements .22
Chapter 2—Basic Properties of Random Vectors.26
2.1 Cumulative distribution functions and probability density func-
tions .26
2.2 Population moments .28
2.3 Characteristic functions.33
2.4 Transformations.35
2.5 The multinormal distribution .36
2.6 Some multivariate generalizations of univariate distributions . 43
2.7 Families of distributions.45
2.8 Random samples.49
2.9 Limit theorems .51
Exercises and complements .53
Chapter 3—Normal Distribution Theory.59
3.1 Characterization and properties .59
3.2 Linear forms .62
3.3 Transformations of normal data matrices .64
3.4 The Wishart distribution .66
CONTENTS xn
3.5 The Hotelling T2distribution . 73
3.6 Mahalanobis distance. 76
3.7 Statistics based on the Wishart distribution . 80
3.8 Other distributions related to the multinomial.85
Exercises and complements.86
Chapter A—Estimation .96
4.1 Likelihood and sufficiency.96
4.2 Maximum likelihood estimation .102
4.3 Other techniques and concepts.109
Exercises and complements .113
Chapter 5—Hypothesis Testing.120
5.1 Introduction.120
5.2 The techniques introduced .123
5.3 The techniques further illustrated .131
*5.4 The Behrens-Fisher problem .142
5.5 Simultaneous confidence intervals .144
5.6 Multivariate hypothesis testing: some general points .147
*5.7 Non-normal data.148
5.8 A non-parametric test for the bivariate two-sample problem . . . 149
Exercises and complements .151
Chapter 6—Multivariate Regression Analysis.157
6.1 Introduction.157
6.2 Maximum likelihood estimation .158
6.3 The general linear hypothesis.161
6.4 Design matrices of degenerate rank.164
6.5 Multiple correlation .167
6.6 Least squares estimation.171
6.7 Discarding of variables .175
Exercises and complements .180
Chapter 7—Econometrics .185
7.1 Introduction.185
7.2 Instrumental variables and two-stage least squares .186
7.3 Simultaneous equation systems.191
7.4 Single-equation estimators .199
7.5 System estimators .203
7.6 Comparison of estimators.208
Exercises and complements .208
Chapter 8—Principal Component Analysis.213
8.1 Introduction.213
8.2 Definition and properties of principal components .214
8.3 Sampling properties of principal components.229
8.4 Testing hypotheses about principal components .233
8.5 Correspondence analysis .237
8.6 Allometry—the measurement of size and shape .239
xiii CONTENTS
8.7 Discarding of variables .242
8.8 Principal component analysis in regression.244
Exercises and complements .246
Chapter 9—Factor Analysis .255
9.1 Introduction.255
9.2 The factor model.256
9.3 Principal factor analysis.261
9.4 Maximum likelihood factor analysis.263
9.5 Goodness of fit test.267
9.6 Rotation of factors.268
9.7 Factor scores .273
9.8 Relationships between factor analysis and principal component
analysis.275
9.9 Analysis of covariance structures.276
Exercises and complements .276
Chapter 10—Canonical Correlation Analysis.281
10.1 Introduction .281
10.2 Mathematical development.282
10.3 Qualitative data and dummy variables.290
10.4 Qualitative and quantative data.293
Exercises and complements .295
Chapter 11—Discriminant Analysis.300
11.1 Introduction.300
11.2 Discrimination when the populations are known.301
11.3 Discrimination under estimation .309
11.4 Is discrimination worthwhile?.318
11.5 Fisher's linear discriminant function.318
11.6 Probabilities of misclassification .320
11.7 Discarding of variables.322
11.8 When does correlation improve discrimination?.324
Exercises and complements .325
Chapter 12—Multivariate Analysis of Variance.333
12.1 Introduction .333
12.2 Formulation of multivariate one-way classification.333
12.3 The likelihood ratio principle.334
12.4 Testing fixed contrasts.337
12.5 Canonical variables and a test of dimensionality.338
12.6 The union intersection approach .348
12.7 Two-way classification.350
Exercises and complements.356
Chapter 13—Cluster Analysis .360
13.1 Introduction.360
13.2 A probabilistic formulation.361
13.3 Hierarchical methods .369
13.4 Distances and similarities .375
CONTENTS Xiv
13.5 Other methods and comparative approach .384
Exercises and complements .386
Chapter 14—Multidimensional Scaling.394
14.1 Introduction .394
14.2 Classical solution .397
14.3 Duality between principal coordinate analysis and principal com-
ponent analysis.404
14.4 Optimal properties of the classical solution and goodness of fit . . 406
14.5 Seriation.409
14.6 Non-metric methods.413
14.7 Goodness of fit measure: Procrustes rotation.416
*14.8 Multi-sample problem and canonical variâtes.419
Exercises and complements .420
Chapter 15—Directional Data .424
15.1 Introduction .424
15.2 Descriptive measures .426
15.3 Basic distributions.428
15.4 Distribution theory .435
15.5 Maximum likelihood estimators for the von Mises-Fisher distribu-
tion .437
15.6 Test of uniformity: the Rayleigh test.439
15.7 Some other problems .441
Exercises and complements .446
Appendix A—Matrix Algebra .452
A.l Introduction .452
A.2 Matrix operations.455
A.3 Further particular matrices and types of matrix .460
A.4 Vector spaces, rank, and linear equations.462
A.5 Linear transformations.465
A.6 Eigenvalues and eigenvectors.466
A.l Quadratic forms and definiteness .474
*A.8 Generalized inverse.476
A.9 Matrix differentiation and maximization problems.478
A.10 Geometrical ideas.481
Appendix B—Univariate Statistics .486
B.l Introduction .486
B.2 Normal distribution.486
B.3 Chi-squared distribution.487
B.4 F and beta variables.487
B.5 t distribution.488
Appendix C—Tables .489
Table C. 1 Upper percentage points of the xl distribution.490
XV CONTENTS
Table C.2 Upper percentage points of the t„ distribution.491
Table C.3 Upper percentage points of the F„1,„2 distribution.492
Table C.4 Upper percentage points 6a of 0(p, vu v2), the largest
eigenvalue of |B - 8(W+B)| = 0 for p = 2.494
References.V 497
List of Main Notations and Abbreviations. 508
Subject Index. 510
Author Index. 519 |
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| series2 | Probability and mathematical statistics |
| spelling | Mardia, Kantilal V. 1935- Verfasser (DE-588)122951913 aut Multivariate analysis K. V. Mardia ; J. T. Kent ; J. M. Bibby Reprint. Amsterdam [u.a.] Acad. Press 2003 XV, 518 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Probability and mathematical statistics Multivariate analysis Multivariate Analyse (DE-588)4040708-1 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Multivariate Analyse (DE-588)4040708-1 s Statistik (DE-588)4056995-0 s 1\p DE-604 Kent, John T. Verfasser (DE-588)128766425 aut Bibby, John M. Verfasser (DE-588)128766468 aut http://www.loc.gov/catdir/description/els031/79040922.html Publisher description http://www.loc.gov/catdir/toc/els031/79040922.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=016844774&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 | Mardia, Kantilal V. 1935- Kent, John T. Bibby, John M. Multivariate analysis Multivariate analysis Multivariate Analyse (DE-588)4040708-1 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4040708-1 (DE-588)4056995-0 |
| title | Multivariate analysis |
| title_auth | Multivariate analysis |
| title_exact_search | Multivariate analysis |
| title_exact_search_txtP | Multivariate analysis |
| title_full | Multivariate analysis K. V. Mardia ; J. T. Kent ; J. M. Bibby |
| title_fullStr | Multivariate analysis K. V. Mardia ; J. T. Kent ; J. M. Bibby |
| title_full_unstemmed | Multivariate analysis K. V. Mardia ; J. T. Kent ; J. M. Bibby |
| title_short | Multivariate analysis |
| title_sort | multivariate analysis |
| topic | Multivariate analysis Multivariate Analyse (DE-588)4040708-1 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Multivariate analysis Multivariate Analyse Statistik |
| url | http://www.loc.gov/catdir/description/els031/79040922.html http://www.loc.gov/catdir/toc/els031/79040922.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016844774&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT mardiakantilalv multivariateanalysis AT kentjohnt multivariateanalysis AT bibbyjohnm multivariateanalysis |