Coordinate-free multivariable statistics: an illustrated geometric progression from Halmos to Gauss and Bayes
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford
Clarendon Press
1987
|
| Series: | Oxford statistical science series
2 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliography and index |
| Physical Description: | XIV, 120 S. graph. Darst. |
| ISBN: | 019852210X |
Staff View
MARC
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| 245 | 1 | 0 | |a Coordinate-free multivariable statistics |b an illustrated geometric progression from Halmos to Gauss and Bayes |c Mervyn Stone |
| 264 | 1 | |a Oxford |b Clarendon Press |c 1987 | |
| 300 | |a XIV, 120 S. |b graph. Darst. | ||
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| 490 | 1 | |a Oxford statistical science series |v 2 | |
| 490 | 0 | |a Oxford science publications | |
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| 650 | 4 | |a Multivariate analysis | |
| 650 | 4 | |a Transformations (Mathematics) | |
| 650 | 4 | |a Vector spaces | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preamble ix
1. Spaces 1
§1. Statistical data 1
§2. Vector space of variables 1
§3. Dual space of evaluators 3
§4. Statistical problems 4
2. Dualities 9
§5. Values and operators 9
§6. Inner products 12
§7. Dual inner product and orthogonal projection 15
§8. Dualtors and their integral representation 19
§9. Inner products as integrals 21
§10. Shadow, marginal, and transformed inner products 25
§11. Singularities 29
§12. Partial ordering of inner products 40
3. Optimizations 43
§13. Gauss s linear model 43
§14. Non singular variance 44
§15. Singular variance 46
§16. Error estimation 48
§17. Equivalent variances 50
§18. Multivariate least squares 52
§19. Alternative least squares projections 56
§20. Conditional estimation in Gauss s linear model 65
§21. Replication in Gauss s linear model 67
§22. Replication and estimated variance 69
§23. Prediction 72
§24. Bayesian optimizations 82
4. Generalized inverses 89
§25. Annihilating and minimal inverses 89
§26. Duals of generalized inverses 94
vii
viii CONTENTS
§27. Review 95
§28. Representations 96
5. Parametrizations 102
§29. Underparameters and overparameters 102
§30. Gauss estimation 103
§31. Bayesian estimation 109
§32. Updating for the Kalman filter 112
References 117
Glossary 118
Index 119
|
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| dewey-full | 519.5/35 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5/35 |
| dewey-search | 519.5/35 |
| dewey-sort | 3519.5 235 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV003656409 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:03:24Z |
| institution | BVB |
| isbn | 019852210X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002328374 |
| oclc_num | 15055343 |
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| physical | XIV, 120 S. graph. Darst. |
| psigel | TUB-nveb |
| publishDate | 1987 |
| publishDateSearch | 1987 |
| publishDateSort | 1987 |
| publisher | Clarendon Press |
| record_format | marc |
| series | Oxford statistical science series |
| series2 | Oxford statistical science series Oxford science publications |
| spelling | Stone, Mervyn Verfasser (DE-588)170353001 aut Coordinate-free multivariable statistics an illustrated geometric progression from Halmos to Gauss and Bayes Mervyn Stone Oxford Clarendon Press 1987 XIV, 120 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Oxford statistical science series 2 Oxford science publications Includes bibliography and index Algèbre linéaire Analyse multivariée Analyse multivariée ram Espaces vectoriels Espaces vectoriels ram Inverse généralisé Statistique Transformations (Mathématiques) Transformations (mathématiques) ram Multivariate analysis Transformations (Mathematics) Vector spaces Multivariate Analyse (DE-588)4040708-1 gnd rswk-swf Multivariate Analyse (DE-588)4040708-1 s DE-604 Oxford statistical science series 2 (DE-604)BV001908661 2 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002328374&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Stone, Mervyn Coordinate-free multivariable statistics an illustrated geometric progression from Halmos to Gauss and Bayes Oxford statistical science series Algèbre linéaire Analyse multivariée Analyse multivariée ram Espaces vectoriels Espaces vectoriels ram Inverse généralisé Statistique Transformations (Mathématiques) Transformations (mathématiques) ram Multivariate analysis Transformations (Mathematics) Vector spaces Multivariate Analyse (DE-588)4040708-1 gnd |
| subject_GND | (DE-588)4040708-1 |
| title | Coordinate-free multivariable statistics an illustrated geometric progression from Halmos to Gauss and Bayes |
| title_auth | Coordinate-free multivariable statistics an illustrated geometric progression from Halmos to Gauss and Bayes |
| title_exact_search | Coordinate-free multivariable statistics an illustrated geometric progression from Halmos to Gauss and Bayes |
| title_full | Coordinate-free multivariable statistics an illustrated geometric progression from Halmos to Gauss and Bayes Mervyn Stone |
| title_fullStr | Coordinate-free multivariable statistics an illustrated geometric progression from Halmos to Gauss and Bayes Mervyn Stone |
| title_full_unstemmed | Coordinate-free multivariable statistics an illustrated geometric progression from Halmos to Gauss and Bayes Mervyn Stone |
| title_short | Coordinate-free multivariable statistics |
| title_sort | coordinate free multivariable statistics an illustrated geometric progression from halmos to gauss and bayes |
| title_sub | an illustrated geometric progression from Halmos to Gauss and Bayes |
| topic | Algèbre linéaire Analyse multivariée Analyse multivariée ram Espaces vectoriels Espaces vectoriels ram Inverse généralisé Statistique Transformations (Mathématiques) Transformations (mathématiques) ram Multivariate analysis Transformations (Mathematics) Vector spaces Multivariate Analyse (DE-588)4040708-1 gnd |
| topic_facet | Algèbre linéaire Analyse multivariée Espaces vectoriels Inverse généralisé Statistique Transformations (Mathématiques) Transformations (mathématiques) Multivariate analysis Transformations (Mathematics) Vector spaces Multivariate Analyse |
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