Approximate Distributions of Order Statistics: With Applications to Nonparametric Statistics
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
New York, NY
Springer New York
1989
|
| Series: | Springer Series in Statistics
|
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | This book is designed as a unified and mathematically rigorous treatment of some recent developments of the asymptotic distribution theory of order statistics (including the extreme order statistics) that are relevant for statistical theory and its applications. Particular emphasis is placed on results concerning the accuracy oflimit theorems, on higher order approximations, and other approximations in quite a general sense. Contrary to the classical limit theorems that primarily concern the weak convergence of distribution functions, our main results will be formulated in terms of the variational and the Hellinger distance. These results will form the proper springboard for the investigation of parametric approximations of nonparametric models of joint distributions of order statistics. The approximating models include normal as well as extreme value models. Several applications will show the usefulness of this approach. Other recent developments in statistics like nonparametric curve estimation and the bootstrap method will be studied as far as order statistics are concerned. 1n connection with this, graphical methods will, to some extent, be explored |
| Physical Description: | 1 Online-Ressource (XII, 355p. 30 illus) |
| ISBN: | 9781461396208 9781461396222 |
| ISSN: | 0172-7397 |
| DOI: | 10.1007/978-1-4613-9620-8 |
Staff View
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Record in the Search Index
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| dewey-ones | 519 - Probabilities and applied mathematics |
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| id | DE-604.BV042420815 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:07Z |
| institution | BVB |
| isbn | 9781461396208 9781461396222 |
| issn | 0172-7397 |
| language | English |
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| spelling | Reiss, R.-D. Verfasser aut Approximate Distributions of Order Statistics With Applications to Nonparametric Statistics by R.-D. Reiss New York, NY Springer New York 1989 1 Online-Ressource (XII, 355p. 30 illus) txt rdacontent c rdamedia cr rdacarrier Springer Series in Statistics 0172-7397 This book is designed as a unified and mathematically rigorous treatment of some recent developments of the asymptotic distribution theory of order statistics (including the extreme order statistics) that are relevant for statistical theory and its applications. Particular emphasis is placed on results concerning the accuracy oflimit theorems, on higher order approximations, and other approximations in quite a general sense. Contrary to the classical limit theorems that primarily concern the weak convergence of distribution functions, our main results will be formulated in terms of the variational and the Hellinger distance. These results will form the proper springboard for the investigation of parametric approximations of nonparametric models of joint distributions of order statistics. The approximating models include normal as well as extreme value models. Several applications will show the usefulness of this approach. Other recent developments in statistics like nonparametric curve estimation and the bootstrap method will be studied as far as order statistics are concerned. 1n connection with this, graphical methods will, to some extent, be explored Statistics Statistics, general Statistik Nichtparametrische Statistik (DE-588)4226777-8 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Asymptotik (DE-588)4126634-1 gnd rswk-swf Ordnungsstatistik (DE-588)4212486-4 gnd rswk-swf Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd rswk-swf Asymptotische Statistik (DE-588)4203167-9 gnd rswk-swf Ordnungsstatistik (DE-588)4212486-4 s Asymptotik (DE-588)4126634-1 s Wahrscheinlichkeitsverteilung (DE-588)4121894-2 s 1\p DE-604 Nichtparametrische Statistik (DE-588)4226777-8 s 2\p DE-604 Statistik (DE-588)4056995-0 s 3\p DE-604 Asymptotische Statistik (DE-588)4203167-9 s 4\p DE-604 https://doi.org/10.1007/978-1-4613-9620-8 Verlag 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 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Reiss, R.-D Approximate Distributions of Order Statistics With Applications to Nonparametric Statistics Statistics Statistics, general Statistik Nichtparametrische Statistik (DE-588)4226777-8 gnd Statistik (DE-588)4056995-0 gnd Asymptotik (DE-588)4126634-1 gnd Ordnungsstatistik (DE-588)4212486-4 gnd Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd Asymptotische Statistik (DE-588)4203167-9 gnd |
| subject_GND | (DE-588)4226777-8 (DE-588)4056995-0 (DE-588)4126634-1 (DE-588)4212486-4 (DE-588)4121894-2 (DE-588)4203167-9 |
| title | Approximate Distributions of Order Statistics With Applications to Nonparametric Statistics |
| title_auth | Approximate Distributions of Order Statistics With Applications to Nonparametric Statistics |
| title_exact_search | Approximate Distributions of Order Statistics With Applications to Nonparametric Statistics |
| title_full | Approximate Distributions of Order Statistics With Applications to Nonparametric Statistics by R.-D. Reiss |
| title_fullStr | Approximate Distributions of Order Statistics With Applications to Nonparametric Statistics by R.-D. Reiss |
| title_full_unstemmed | Approximate Distributions of Order Statistics With Applications to Nonparametric Statistics by R.-D. Reiss |
| title_short | Approximate Distributions of Order Statistics |
| title_sort | approximate distributions of order statistics with applications to nonparametric statistics |
| title_sub | With Applications to Nonparametric Statistics |
| topic | Statistics Statistics, general Statistik Nichtparametrische Statistik (DE-588)4226777-8 gnd Statistik (DE-588)4056995-0 gnd Asymptotik (DE-588)4126634-1 gnd Ordnungsstatistik (DE-588)4212486-4 gnd Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd Asymptotische Statistik (DE-588)4203167-9 gnd |
| topic_facet | Statistics Statistics, general Statistik Nichtparametrische Statistik Asymptotik Ordnungsstatistik Wahrscheinlichkeitsverteilung Asymptotische Statistik |
| url | https://doi.org/10.1007/978-1-4613-9620-8 |
| work_keys_str_mv | AT reissrd approximatedistributionsoforderstatisticswithapplicationstononparametricstatistics |