Comparison of statistical experiments:
There are a number of important questions associated with statistical experiments: when does one given experiment yield more information than another; how can we measure the difference in information; how fast does information accumulate by repeating the experiment? The means of answering such quest...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
1990
|
| Schriftenreihe: | Encyclopedia of mathematics and its applications
volume 36 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 Volltext |
| Zusammenfassung: | There are a number of important questions associated with statistical experiments: when does one given experiment yield more information than another; how can we measure the difference in information; how fast does information accumulate by repeating the experiment? The means of answering such questions has emerged from the work of Wald, Blackwell, LeCam and others and is based on the ideas of risk and deficiency. The present work which is devoted to the various methods of comparing statistical experiments, is essentially self-contained, requiring only some background in measure theory and functional analysis. Chapters introducing statistical experiments and the necessary convex analysis begin the book and are followed by others on game theory, decision theory and vector lattices. The notion of deficiency, which measures the difference in information between two experiments, is then introduced. The relation between it and other concepts, such as sufficiency, randomisation, distance, ordering, equivalence, completeness and convergence are explored. This is a comprehensive treatment of the subject and will be an essential reference for mathematical statisticians |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (xx, 675 pages) |
| ISBN: | 9780511666353 |
| DOI: | 10.1017/CBO9780511666353 |
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| 505 | 8 | |a Statistical experiments within the measure theoretical framework -- Convexity -- Two-person, zero-sum games -- Statistical decision problems -- Vector lattices -- Deficiencies -- Equivalence, representations and functionals of experiments -- Comparison of linear models -- Majorization and approximate majorization -- Complements: further examples, problems and comments | |
| 520 | |a There are a number of important questions associated with statistical experiments: when does one given experiment yield more information than another; how can we measure the difference in information; how fast does information accumulate by repeating the experiment? The means of answering such questions has emerged from the work of Wald, Blackwell, LeCam and others and is based on the ideas of risk and deficiency. The present work which is devoted to the various methods of comparing statistical experiments, is essentially self-contained, requiring only some background in measure theory and functional analysis. Chapters introducing statistical experiments and the necessary convex analysis begin the book and are followed by others on game theory, decision theory and vector lattices. The notion of deficiency, which measures the difference in information between two experiments, is then introduced. The relation between it and other concepts, such as sufficiency, randomisation, distance, ordering, equivalence, completeness and convergence are explored. This is a comprehensive treatment of the subject and will be an essential reference for mathematical statisticians | ||
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Datensatz im Suchindex
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| author | Torgersen, Erik N. |
| author_facet | Torgersen, Erik N. |
| author_role | aut |
| author_sort | Torgersen, Erik N. |
| author_variant | e n t en ent |
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| contents | Statistical experiments within the measure theoretical framework -- Convexity -- Two-person, zero-sum games -- Statistical decision problems -- Vector lattices -- Deficiencies -- Equivalence, representations and functionals of experiments -- Comparison of linear models -- Majorization and approximate majorization -- Complements: further examples, problems and comments |
| ctrlnum | (ZDB-20-CBO)CR9780511666353 (OCoLC)967601407 (DE-599)BVBBV043941763 |
| dewey-full | 519.5/42 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5/42 |
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| dewey-sort | 3519.5 242 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| doi_str_mv | 10.1017/CBO9780511666353 |
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| isbn | 9780511666353 |
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| spelling | Torgersen, Erik N. Verfasser aut Comparison of statistical experiments Erik Torgersen Cambridge Cambridge University Press 1990 1 online resource (xx, 675 pages) txt rdacontent c rdamedia cr rdacarrier Encyclopedia of mathematics and its applications volume 36 Title from publisher's bibliographic system (viewed on 05 Oct 2015) Statistical experiments within the measure theoretical framework -- Convexity -- Two-person, zero-sum games -- Statistical decision problems -- Vector lattices -- Deficiencies -- Equivalence, representations and functionals of experiments -- Comparison of linear models -- Majorization and approximate majorization -- Complements: further examples, problems and comments There are a number of important questions associated with statistical experiments: when does one given experiment yield more information than another; how can we measure the difference in information; how fast does information accumulate by repeating the experiment? The means of answering such questions has emerged from the work of Wald, Blackwell, LeCam and others and is based on the ideas of risk and deficiency. The present work which is devoted to the various methods of comparing statistical experiments, is essentially self-contained, requiring only some background in measure theory and functional analysis. Chapters introducing statistical experiments and the necessary convex analysis begin the book and are followed by others on game theory, decision theory and vector lattices. The notion of deficiency, which measures the difference in information between two experiments, is then introduced. The relation between it and other concepts, such as sufficiency, randomisation, distance, ordering, equivalence, completeness and convergence are explored. This is a comprehensive treatment of the subject and will be an essential reference for mathematical statisticians Statistical decision Mathematical statistics Experiment (DE-588)4015999-1 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Statistische Entscheidungstheorie (DE-588)4077850-2 gnd rswk-swf 1\p (DE-588)4143413-4 Aufsatzsammlung gnd-content Experiment (DE-588)4015999-1 s Statistik (DE-588)4056995-0 s 2\p DE-604 Statistische Entscheidungstheorie (DE-588)4077850-2 s 3\p DE-604 Erscheint auch als Druckausgabe 978-0-521-10282-7 Erscheint auch als Druckausgabe 978-0-521-25030-6 https://doi.org/10.1017/CBO9780511666353 Verlag URL des Erstveröffentlichers Volltext 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 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Torgersen, Erik N. Comparison of statistical experiments Statistical experiments within the measure theoretical framework -- Convexity -- Two-person, zero-sum games -- Statistical decision problems -- Vector lattices -- Deficiencies -- Equivalence, representations and functionals of experiments -- Comparison of linear models -- Majorization and approximate majorization -- Complements: further examples, problems and comments Statistical decision Mathematical statistics Experiment (DE-588)4015999-1 gnd Statistik (DE-588)4056995-0 gnd Statistische Entscheidungstheorie (DE-588)4077850-2 gnd |
| subject_GND | (DE-588)4015999-1 (DE-588)4056995-0 (DE-588)4077850-2 (DE-588)4143413-4 |
| title | Comparison of statistical experiments |
| title_auth | Comparison of statistical experiments |
| title_exact_search | Comparison of statistical experiments |
| title_full | Comparison of statistical experiments Erik Torgersen |
| title_fullStr | Comparison of statistical experiments Erik Torgersen |
| title_full_unstemmed | Comparison of statistical experiments Erik Torgersen |
| title_short | Comparison of statistical experiments |
| title_sort | comparison of statistical experiments |
| topic | Statistical decision Mathematical statistics Experiment (DE-588)4015999-1 gnd Statistik (DE-588)4056995-0 gnd Statistische Entscheidungstheorie (DE-588)4077850-2 gnd |
| topic_facet | Statistical decision Mathematical statistics Experiment Statistik Statistische Entscheidungstheorie Aufsatzsammlung |
| url | https://doi.org/10.1017/CBO9780511666353 |
| work_keys_str_mv | AT torgersenerikn comparisonofstatisticalexperiments |