Contiguity of probability measures: some applications in statistics:
This Tract presents an elaboration of the notion of 'contiguity', which is a concept of 'nearness' of sequences of probability measures. It provides a powerful mathematical tool for establishing certain theoretical results with applications in statistics, particularly in large sa...
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
1972
|
| Series: | Cambridge tracts in mathematics
63 |
| Subjects: | |
| Online Access: | BSB01 FHN01 UBR01 Volltext |
| Summary: | This Tract presents an elaboration of the notion of 'contiguity', which is a concept of 'nearness' of sequences of probability measures. It provides a powerful mathematical tool for establishing certain theoretical results with applications in statistics, particularly in large sample theory problems, where it simplifies derivations and points the way to important results. The potential of this concept has so far only been touched upon in the existing literature, and this book provides the first systematic discussion of it. Alternative characterizations of contiguity are first described and related to more familiar mathematical ideas of a similar nature. A number of general theorems are formulated and proved. These results, which provide the means of obtaining asymptotic expansions and distributions of likelihood functions, are essential to the applications which follow |
| Physical Description: | 1 Online-Ressource (xiii, 248 Seiten) |
| ISBN: | 9780511804373 |
| DOI: | 10.1017/CBO9780511804373 |
Staff View
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| 490 | 0 | |a Cambridge tracts in mathematics |v 63 | |
| 505 | 8 | |a On the concept of contiguity and related theorems -- Asymptotic expansions and asymptotic distribution of likelihood functions -- Approximation of a given family of probability measures by an exponential family, asymptotic sufficiency -- Some statistical applications, AUMP and AUMPU test for certain testing hypotheses problems -- Some statistical applications, asymptotic efficiency of estimates -- Multiparameter asymptotically optimal tests | |
| 520 | |a This Tract presents an elaboration of the notion of 'contiguity', which is a concept of 'nearness' of sequences of probability measures. It provides a powerful mathematical tool for establishing certain theoretical results with applications in statistics, particularly in large sample theory problems, where it simplifies derivations and points the way to important results. The potential of this concept has so far only been touched upon in the existing literature, and this book provides the first systematic discussion of it. Alternative characterizations of contiguity are first described and related to more familiar mathematical ideas of a similar nature. A number of general theorems are formulated and proved. These results, which provide the means of obtaining asymptotic expansions and distributions of likelihood functions, are essential to the applications which follow | ||
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| author | Roussas, George G. 1933- |
| author_GND | (DE-588)122639596 |
| author_facet | Roussas, George G. 1933- |
| author_role | aut |
| author_sort | Roussas, George G. 1933- |
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| contents | On the concept of contiguity and related theorems -- Asymptotic expansions and asymptotic distribution of likelihood functions -- Approximation of a given family of probability measures by an exponential family, asymptotic sufficiency -- Some statistical applications, AUMP and AUMPU test for certain testing hypotheses problems -- Some statistical applications, asymptotic efficiency of estimates -- Multiparameter asymptotically optimal tests |
| ctrlnum | (ZDB-20-CBO)CR9780511804373 (OCoLC)849880157 (DE-599)BVBBV043942310 |
| dewey-full | 519.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 |
| dewey-search | 519.2 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| doi_str_mv | 10.1017/CBO9780511804373 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:17Z |
| institution | BVB |
| isbn | 9780511804373 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029351280 |
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| owner_facet | DE-12 DE-92 DE-355 DE-BY-UBR |
| physical | 1 Online-Ressource (xiii, 248 Seiten) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO ZDB-20-CBO UBR Einzelkauf (Lückenergänzung CUP Serien 2018) |
| publishDate | 1972 |
| publishDateSearch | 1972 |
| publishDateSort | 1972 |
| publisher | Cambridge University Press |
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| series2 | Cambridge tracts in mathematics |
| spelling | Roussas, George G. 1933- Verfasser (DE-588)122639596 aut Contiguity of probability measures: some applications in statistics George G. Roussas Cambridge Cambridge University Press 1972 1 Online-Ressource (xiii, 248 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge tracts in mathematics 63 On the concept of contiguity and related theorems -- Asymptotic expansions and asymptotic distribution of likelihood functions -- Approximation of a given family of probability measures by an exponential family, asymptotic sufficiency -- Some statistical applications, AUMP and AUMPU test for certain testing hypotheses problems -- Some statistical applications, asymptotic efficiency of estimates -- Multiparameter asymptotically optimal tests This Tract presents an elaboration of the notion of 'contiguity', which is a concept of 'nearness' of sequences of probability measures. It provides a powerful mathematical tool for establishing certain theoretical results with applications in statistics, particularly in large sample theory problems, where it simplifies derivations and points the way to important results. The potential of this concept has so far only been touched upon in the existing literature, and this book provides the first systematic discussion of it. Alternative characterizations of contiguity are first described and related to more familiar mathematical ideas of a similar nature. A number of general theorems are formulated and proved. These results, which provide the means of obtaining asymptotic expansions and distributions of likelihood functions, are essential to the applications which follow Probability measures Mathematical statistics Wahrscheinlichkeitsmaß (DE-588)4137556-7 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Wahrscheinlichkeitsmaß (DE-588)4137556-7 s Statistik (DE-588)4056995-0 s DE-604 Erscheint auch als Druck-Ausgabe 978-0-521-08354-6 Erscheint auch als Druck-Ausgabe 978-0-521-09095-7 https://doi.org/10.1017/CBO9780511804373 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Roussas, George G. 1933- Contiguity of probability measures: some applications in statistics On the concept of contiguity and related theorems -- Asymptotic expansions and asymptotic distribution of likelihood functions -- Approximation of a given family of probability measures by an exponential family, asymptotic sufficiency -- Some statistical applications, AUMP and AUMPU test for certain testing hypotheses problems -- Some statistical applications, asymptotic efficiency of estimates -- Multiparameter asymptotically optimal tests Probability measures Mathematical statistics Wahrscheinlichkeitsmaß (DE-588)4137556-7 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4137556-7 (DE-588)4056995-0 |
| title | Contiguity of probability measures: some applications in statistics |
| title_auth | Contiguity of probability measures: some applications in statistics |
| title_exact_search | Contiguity of probability measures: some applications in statistics |
| title_full | Contiguity of probability measures: some applications in statistics George G. Roussas |
| title_fullStr | Contiguity of probability measures: some applications in statistics George G. Roussas |
| title_full_unstemmed | Contiguity of probability measures: some applications in statistics George G. Roussas |
| title_short | Contiguity of probability measures: some applications in statistics |
| title_sort | contiguity of probability measures some applications in statistics |
| topic | Probability measures Mathematical statistics Wahrscheinlichkeitsmaß (DE-588)4137556-7 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Probability measures Mathematical statistics Wahrscheinlichkeitsmaß Statistik |
| url | https://doi.org/10.1017/CBO9780511804373 |
| work_keys_str_mv | AT roussasgeorgeg contiguityofprobabilitymeasuressomeapplicationsinstatistics |