Theory of multivariate statistics:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
1999
|
| Series: | Springer texts in statistics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 288 S. graph. Darst. |
| ISBN: | 0387987398 |
Staff View
MARC
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| 245 | 1 | 0 | |a Theory of multivariate statistics |c Martin Bilodeau ; David Brenner |
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Record in the Search Index
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| adam_text | Contents
Preface vii
List of Tables xv
List of Figures xvii
1 Linear algebra 1
1.1 Introduction 1
1.2 Vectors and matrices 1
1.3 Image space and kernel 3
1.4 Nonsingular matrices and determinants 4
1.5 Eigenvalues and eigenvectors 5
1.6 Orthogonal projections 9
1.7 Matrix decompositions 10
1.8 Problems 11
2 Random vectors 14
2.1 Introduction 14
2.2 Distribution functions 14
2.3 Equals in distribution 16
2.4 Discrete distributions 16
2.5 Expected values 17
2.6 Mean and variance 18
2.7 Characteristic functions 21
2.8 Absolutely continuous distributions 22
2.9 Uniform distributions 24
xii Contents
2.10 Joints and marginals 25
2.11 Independence 27
2.12 Change of variables 28
2.13 Jacobians 30
2.14 Problems 33
3 Gamma, Dirichlet, and F distributions 36
3.1 Introduction 36
3.2 Gamma distributions 36
3.3 Dirichlet distributions 38
3.4 F distributions 42
3.5 Problems 42
4 Invariance 43
4.1 Introduction 43
4.2 Reflection symmetry 43
4.3 Univariate normal and related distributions 44
4.4 Permutation invariance 47
4.5 Orthogonal invariance 48
4.6 Problems 52
5 Multivariate normal 55
5.1 Introduction 55
5.2 Definition and elementary properties 55
5.3 Nonsingular normal 58
5.4 Singular normal 62
5.5 Conditional normal 62
5.6 Elementary applications 64
5.6.1 Sampling the univariate normal 64
5.6.2 Linear estimation 65
5.6.3 Simple correlation 67
5.7 Problems 69
6 Multivariate sampling 73
6.1 Introduction 73
6.2 Random matrices and multivariate sample 73
6.3 Asymptotic distributions 78
6.4 Problems 81
7 Wishart distributions 85
7.1 Introduction 85
7.2 Joint distribution of x and S 85
7.3 Properties of Wishart distributions 87
7.4 Box Cox transformations 94
7.5 Problems 96
Contents xiii
8 Tests on mean and variance 98
8.1 Introduction 98
8.2 Hotelling r2 98
8.3 Simultaneous confidence intervals on means 104
8.3.1 Linear hypotheses 104
8.3.2 Nonlinear hypotheses 107
8.4 Multiple correlation 109
8.4.1 Asymptotic moments 114
8.5 Partial correlation 116
8.6 Test of sphericity 117
8.7 Test of equality of variances 121
8.8 Asymptotic distributions of eigenvalues 124
8.8.1 The one sample problem 124
8.8.2 The two sample problem 132
8.8.3 The case of multiple eigenvalues 133
8.9 Problems 137
9 Multivariate regression 144
9.1 Introduction 144
9.2 Estimation 145
9.3 The general linear hypothesis 148
9.3.1 Canonical form 148
9.3.2 LRT for the canonical problem 150
9.3.3 Invariant tests 151
9.4 Random design matrix X 154
9.5 Predictions 156
9.6 One way classification 158
9.7 Problems 159
10 Principal components 161
10.1 Introduction 161
10.2 Definition and basic properties 162
10.3 Best approximating subspace 163
10.4 Sample principal components from S 164
10.5 Sample principal components from R 166
10.6 A test for multivariate normality 169
10.7 Problems 172
11 Canonical correlations 174
11.1 Introduction 174
11.2 Definition and basic properties 175
11.3 Tests of independence 177
11.4 Properties of U distributions 181
11.4.1 Q Q plot of squared radii 184
xiv Contents
11.5 Asymptotic distributions 189
11.6 Problems 190
12 Asymptotic expansions 195
12.1 Introduction 195
12.2 General expansions 195
12.3 Examples 200
12.4 Problem 205
13 Robustness 206
13.1 Introduction 206
13.2 Elliptical distributions 207
13.3 Maximum likelihood estimates 213
13.3.1 Normal MLE 213
13.3.2 Elliptical MLE 213
13.4 Robust estimates 222
13.4.1 M estimate 222
13.4.2 S estimate 224
13.4.3 Robust Hotelling T2 226
13.5 Robust tests on scale matrices 227
13.5.1 Adjusted likelihood ratio tests 228
13.5.2 Weighted Nagao s test for a given variance .... 233
13.5.3 Relative efficiency of adjusted LRT 236
13.6 Problems 238
14 Bootstrap confidence regions and tests 243
14.1 Confidence regions and tests for the mean 243
14.2 Confidence regions for the variance 246
14.3 Tests on the variance 249
14.4 Problem 252
A Inversion formulas 253
B Multivariate cumulants 256
B.I Definition and properties 256
B.2 Application to asymptotic distributions 259
B.3 Problems 259
C S plus functions 261
References 263
Author Index 277
Subject Index 281
|
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
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| dewey-search | 519.535 519.5/35 21 |
| dewey-sort | 3519.535 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:31:54Z |
| institution | BVB |
| isbn | 0387987398 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008621674 |
| oclc_num | 245926991 |
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| physical | XIV, 288 S. graph. Darst. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer texts in statistics |
| spelling | Bilodeau, Martin 1961- Verfasser (DE-588)121395820 aut Theory of multivariate statistics Martin Bilodeau ; David Brenner New York [u.a.] Springer 1999 XIV, 288 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer texts in statistics Multivariate Analyse - Lehrbuch Multivariate analysis Multivariate Analyse (DE-588)4040708-1 gnd rswk-swf Multivariate Analyse (DE-588)4040708-1 s DE-604 Brenner, David 1946- Verfasser (DE-588)1196646074 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008621674&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bilodeau, Martin 1961- Brenner, David 1946- Theory of multivariate statistics Multivariate Analyse - Lehrbuch Multivariate analysis Multivariate Analyse (DE-588)4040708-1 gnd |
| subject_GND | (DE-588)4040708-1 |
| title | Theory of multivariate statistics |
| title_auth | Theory of multivariate statistics |
| title_exact_search | Theory of multivariate statistics |
| title_full | Theory of multivariate statistics Martin Bilodeau ; David Brenner |
| title_fullStr | Theory of multivariate statistics Martin Bilodeau ; David Brenner |
| title_full_unstemmed | Theory of multivariate statistics Martin Bilodeau ; David Brenner |
| title_short | Theory of multivariate statistics |
| title_sort | theory of multivariate statistics |
| topic | Multivariate Analyse - Lehrbuch Multivariate analysis Multivariate Analyse (DE-588)4040708-1 gnd |
| topic_facet | Multivariate Analyse - Lehrbuch Multivariate analysis Multivariate Analyse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008621674&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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