The linear hypothesis: a general theory
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London [u.a.]
Griffin
1980
|
| Edition: | 2. ed. |
| Series: | Griffin's statistical monograph series
19 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 117 S. |
| ISBN: | 0852642571 |
Staff View
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| 100 | 1 | |a Seber, George A. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a The linear hypothesis |b a general theory |c G. A. F. Seber |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a London [u.a.] |b Griffin |c 1980 | |
| 300 | |a X, 117 S. | ||
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Record in the Search Index
| _version_ | 1804120327751467008 |
|---|---|
| adam_text | CONTENTS
Chapter Page
1 PRELIMINARIES
1.1 Notation 1
1.2 The linear vector space 1
1.3 Basis of a vector space 2
1.4 Addition and intersection of vector spaces 3
1.5 Idempotent matrices 3
1.6 Covariance of vectors 4
1.7 The multivariate normal distribution 4
1.8 The non-central chi-squared distribution 5
1.9 Quadratic forms 6
1.10 The non-central F- and Beta distributions 8
1.11 Lagrange multipliers 9
1.12 Additional references 9
2 THE LINEAR HYPOTHESIS
2.1 Regression analysis 10
2.2 Analysis of variance 10
2.3 General definition 11
3 LEAST SQUARES ESTIMATION
3.1 Principle of least squares 13
3.2 Projection matrices 14
3.3 A useful lemma 15
3.4 Examples 18
3.5 Gauss-Markov theorem 18
3.6 The logic of least squares 19
3.7 Estimation of o-2 20
3.8 Related topics 21
4 HYPOTHESIS TESTING
4.1 Maximum likelihood estimation 23
4.2 TheF-test 24
4.3 A canonical form 27
4.4 The Wald principle 27
4.5 Contrasts 29
4.6 Confidence regions 31
4.7 Additional references 32
5 PROPERTIES OF THE F-TEST
5.1 Power of the F-test 34
5.2 Robustness 38
6 TESTING SEVERAL HYPOTHESES
6.1 The nested procedure 40
6.2 Orthogonality 42
ix
6.3 Orthogonality in complete two-way layouts 45
6.4 Complete higher-way layouts 51
6.5 Orthogonality in experimental designs 53
6.6 Orthogonal polynomials 56
6.7 The use of principal components in regression 56
6.8 Non-orthogonal hypotheses 57
6.9 Additional references 58
7 MODIFIED HYPOTHESES
7.1 Least squares estimation 59
7.2 Hypothesis testing 60
7.3 Analysis of covariance 61
7.4 Addition of extra variables in regression 65
8 MISSING OBSERVATIONS
8.1 Estimation 67.
8.2 Hypothesis testing 69
8.3 Correction for bias 69
8.4 An example 70
8.5 An approximate test 71
8.6 Analysis of covariance method 72
8.7 Application to regression analysis 73
8.8 Additional references and related topics 74
9 MULTIVARIATE LINEAR HYPOTHESES
9.1 Introduction 76
9.2 Test statistics 79
9.3 Examples 82
9.4 Testing several hypotheses 85
9.5 Analysis of covariance 86
9.6 Additional references 87
10 NON-LINEAR NORMAL MODELS
10.1 Notation and assumptions 88
10.2 Least squares estimation 89
10.3 Properties of the estimates 91
10.4 Exact confidence regions and hypothesis tests 91
10.5 Further references 93
11 LARGE SAMPLE THEORY FOR NON-LINEAR HYPOTHESES
11.1 Introduction 94
11.2 Notation 94
11.3 Maximum likelihood equations 96
11.4 The linear model approximation 98
11.5 The three test statistics 100
APPENDICES 103
REFERENCES 106
INDEX 115
|
| any_adam_object | 1 |
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| ctrlnum | (OCoLC)611059387 (DE-599)BVBBV006103372 |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 2. ed. |
| format | Book |
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| spelling | Seber, George A. Verfasser aut The linear hypothesis a general theory G. A. F. Seber 2. ed. London [u.a.] Griffin 1980 X, 117 S. txt rdacontent n rdamedia nc rdacarrier Griffin's statistical monograph series 19 Analyse de régression ram Analyse multivariée ram Statistique mathématique ram Tests d'hypothèses (statistique) ram Statistical hypothesis testing Statistische Hypothese (DE-588)4182959-1 gnd rswk-swf Lineares System (DE-588)4125617-7 gnd rswk-swf Entscheidungstheorie (DE-588)4138606-1 gnd rswk-swf Markov-Prozess (DE-588)4134948-9 gnd rswk-swf Schätztheorie (DE-588)4121608-8 gnd rswk-swf Markov-Prozess (DE-588)4134948-9 s DE-604 Schätztheorie (DE-588)4121608-8 s Entscheidungstheorie (DE-588)4138606-1 s Lineares System (DE-588)4125617-7 s 1\p DE-604 Statistische Hypothese (DE-588)4182959-1 s 2\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003855192&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Seber, George A. The linear hypothesis a general theory Analyse de régression ram Analyse multivariée ram Statistique mathématique ram Tests d'hypothèses (statistique) ram Statistical hypothesis testing Statistische Hypothese (DE-588)4182959-1 gnd Lineares System (DE-588)4125617-7 gnd Entscheidungstheorie (DE-588)4138606-1 gnd Markov-Prozess (DE-588)4134948-9 gnd Schätztheorie (DE-588)4121608-8 gnd |
| subject_GND | (DE-588)4182959-1 (DE-588)4125617-7 (DE-588)4138606-1 (DE-588)4134948-9 (DE-588)4121608-8 |
| title | The linear hypothesis a general theory |
| title_auth | The linear hypothesis a general theory |
| title_exact_search | The linear hypothesis a general theory |
| title_full | The linear hypothesis a general theory G. A. F. Seber |
| title_fullStr | The linear hypothesis a general theory G. A. F. Seber |
| title_full_unstemmed | The linear hypothesis a general theory G. A. F. Seber |
| title_short | The linear hypothesis |
| title_sort | the linear hypothesis a general theory |
| title_sub | a general theory |
| topic | Analyse de régression ram Analyse multivariée ram Statistique mathématique ram Tests d'hypothèses (statistique) ram Statistical hypothesis testing Statistische Hypothese (DE-588)4182959-1 gnd Lineares System (DE-588)4125617-7 gnd Entscheidungstheorie (DE-588)4138606-1 gnd Markov-Prozess (DE-588)4134948-9 gnd Schätztheorie (DE-588)4121608-8 gnd |
| topic_facet | Analyse de régression Analyse multivariée Statistique mathématique Tests d'hypothèses (statistique) Statistical hypothesis testing Statistische Hypothese Lineares System Entscheidungstheorie Markov-Prozess Schätztheorie |
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