Generalized inverse matrices with applications to statistics
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| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London
Griffin
1971
|
| Schriftenreihe: | Griffin's statistical monographs and courses. No.28.
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
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| 100 | 1 | |a Pringle, Robert M. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Generalized inverse matrices with applications to statistics |c Robert M. Pringle ; Arthur A. Rayner* |
| 264 | 1 | |a London |b Griffin |c 1971 | |
| 300 | |a VIII,127 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Griffin's statistical monographs and courses. No.28. | |
| 650 | 4 | |a Analyse de variance | |
| 650 | 4 | |a Análisis estadístico multivariable | |
| 650 | 4 | |a Matrices - Inversion | |
| 650 | 4 | |a Analysis of variance | |
| 650 | 4 | |a Matrix inversion | |
| 650 | 0 | 7 | |a Verallgemeinerung |0 (DE-588)4316262-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Inverse Matrix |0 (DE-588)4162224-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Verallgemeinerte Inverse |0 (DE-588)4187511-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Statistik |0 (DE-588)4056995-0 |2 gnd |9 rswk-swf |
| 655 | 7 | |a Verallgemeinerte inverse Matrix |2 gnd |9 rswk-swf | |
| 689 | 0 | 0 | |a Statistik |0 (DE-588)4056995-0 |D s |
| 689 | 0 | 1 | |a Verallgemeinerte inverse Matrix |A f |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Inverse Matrix |0 (DE-588)4162224-8 |D s |
| 689 | 1 | 1 | |a Verallgemeinerung |0 (DE-588)4316262-9 |D s |
| 689 | 1 | |5 DE-604 | |
| 689 | 2 | 0 | |a Verallgemeinerte Inverse |0 (DE-588)4187511-4 |D s |
| 689 | 2 | 1 | |a Statistik |0 (DE-588)4056995-0 |D s |
| 689 | 2 | |5 DE-604 | |
| 689 | 3 | 0 | |a Verallgemeinerte Inverse |0 (DE-588)4187511-4 |D s |
| 689 | 3 | |5 DE-604 | |
| 700 | 1 | |a Rayner, Arthur A. |e Verfasser |4 aut | |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-003119196 | |
Datensatz im Suchindex
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|---|---|
| DE-19_location | 70 |
| DE-BY-UBM_katkey | 2510677 |
| DE-BY-UBM_media_number | 41621875030017 |
| _version_ | 1823052162324758528 |
| adam_text | CONTENTS
Chapter Page
1 DEFINITIONS AND SOME PRELIMINARY RESULTS 1
1.1 Notation and general introduction 1
1.2 The generalized inverse 3
1.3 One condition generalized inverses 6
1.4 Solution of linear equations 9
1.5 Two condition generalized inverses 12
1.6 Three condition generalized inverses 15
1.7 Discussion 15
2 THEORETICAL PROPERTIES OF GENERALIZED
INVERSES 17
2.1 Introduction 17
2.2 Results on rank and idempotency 17
2.3 Results on symmetry 18
2.4 Commuting generalized inverses 19
2.5 Latent roots and vectors 23
2.6 Relationships between types of generalized
inverses 24
2.7 Generalized inverses of product matrices 30
2.8 Special results on g, inverses 32
2.9 Miscellaneous results 35
3 GENERALIZED INVERSES OF PARTITIONED AND
BORDERED MATRICES 37
3.1 Introduction 37
3.2 Matrices partitioned into two submatrices 38
3.3 Partitioned positive semidefinite matrices 45
3.4 Bordered matrices 48
3.5 Some remarks on generalized inverses of partitioned
and bordered matrices 53
4 METHODS OF COMPUTING GENERALIZED INVERSES 55
4.1 Introduction 55
4.2 The g inverse 56
vii
Chapter Page
4.3 g, inverses 61
4.4 g2 inverses 66
4.5 g3 inverses 67
4.6 The Cholesky technique 67
5 SINGULAR NORMAL VARIATES 70
5.1 Conditional means and variances of the normal
multivariate distribution 70
5.2 Regression properties of the multivariate normal
distribution 72
5.3 Reversible transformations of singular to nonsingular
variates 74
5.4 Conditions for a second degree polynomial in normal
variates to have noncentral x2 distribution 77
6 THE LINEAR MODEL OF LESS THAN FULL RANK 80
6.1 Introduction 80
6.2 Estimable linear functions 81
6.3 The method of imposed linear restrictions 90
6.4 Relationship between estimability and linear restrictions 93
6.5 Linear models with a priori linear constraints 98
6.6 Some aspects of partitioned linear models 101
6.7 Some statistical interpretations of g inverses in linear
estimation procedures 106
7 THE LINEAR MODEL WITH SINGULAR VARIANCE
MATRIX 109
7.1 Introduction 109
7.2 The Goldman Zelen method 110
7.3 The Zyskind Martin method 114
CONCLUDING REMARKS 118
REFERENCES 119
INDEX 125
|
| any_adam_object | 1 |
| author | Pringle, Robert M. Rayner, Arthur A. |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.943 |
| dewey-search | 512/.943 |
| dewey-sort | 3512 3943 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| genre | Verallgemeinerte inverse Matrix gnd |
| genre_facet | Verallgemeinerte inverse Matrix |
| id | DE-604.BV005088243 |
| illustrated | Not Illustrated |
| indexdate | 2025-02-03T16:44:36Z |
| institution | BVB |
| isbn | 0852641818 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003119196 |
| oclc_num | 226631 |
| open_access_boolean | |
| owner | DE-703 DE-19 DE-BY-UBM |
| owner_facet | DE-703 DE-19 DE-BY-UBM |
| physical | VIII,127 S. |
| publishDate | 1971 |
| publishDateSearch | 1971 |
| publishDateSort | 1971 |
| publisher | Griffin |
| record_format | marc |
| series2 | Griffin's statistical monographs and courses. No.28. |
| spellingShingle | Pringle, Robert M. Rayner, Arthur A. Generalized inverse matrices with applications to statistics Analyse de variance Análisis estadístico multivariable Matrices - Inversion Analysis of variance Matrix inversion Verallgemeinerung (DE-588)4316262-9 gnd Inverse Matrix (DE-588)4162224-8 gnd Verallgemeinerte Inverse (DE-588)4187511-4 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4316262-9 (DE-588)4162224-8 (DE-588)4187511-4 (DE-588)4056995-0 |
| title | Generalized inverse matrices with applications to statistics |
| title_auth | Generalized inverse matrices with applications to statistics |
| title_exact_search | Generalized inverse matrices with applications to statistics |
| title_full | Generalized inverse matrices with applications to statistics Robert M. Pringle ; Arthur A. Rayner* |
| title_fullStr | Generalized inverse matrices with applications to statistics Robert M. Pringle ; Arthur A. Rayner* |
| title_full_unstemmed | Generalized inverse matrices with applications to statistics Robert M. Pringle ; Arthur A. Rayner* |
| title_short | Generalized inverse matrices with applications to statistics |
| title_sort | generalized inverse matrices with applications to statistics |
| topic | Analyse de variance Análisis estadístico multivariable Matrices - Inversion Analysis of variance Matrix inversion Verallgemeinerung (DE-588)4316262-9 gnd Inverse Matrix (DE-588)4162224-8 gnd Verallgemeinerte Inverse (DE-588)4187511-4 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Analyse de variance Análisis estadístico multivariable Matrices - Inversion Analysis of variance Matrix inversion Verallgemeinerung Inverse Matrix Verallgemeinerte Inverse Statistik Verallgemeinerte inverse Matrix |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003119196&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT pringlerobertm generalizedinversematriceswithapplicationstostatistics AT raynerarthura generalizedinversematriceswithapplicationstostatistics |