Weighted Empirical Processes in Dynamic Nonlinear Models:
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
New York, NY
Springer New York
2002
|
| Edition: | Second Edition |
| Series: | Lecture Notes in Statistics
166 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | The role of the weak convergence technique via weighted empirical processes has proved to be very useful in advancing the development of the asymptotic theory of the so called robust inference procedures corresponding to non-smooth score functions from linear models to nonlinear dynamic models in the 1990's. This monograph is an ex panded version of the monograph Weighted Empiricals and Linear Models, IMS Lecture Notes-Monograph, 21 published in 1992, that includes some aspects of this development. The new inclusions are as follows. Theorems 2. 2. 4 and 2. 2. 5 give an extension of the Theorem 2. 2. 3 (old Theorem 2. 2b. 1) to the unbounded random weights case. These results are found useful in Chapters 7 and 8 when dealing with ho moscedastic and conditionally heteroscedastic autoregressive models, actively researched family of dynamic models in time series analysis in the 1990's. The weak convergence results pertaining to the partial sum process given in Theorems 2. 2. 6 . and 2. 2. 7 are found useful in fitting a parametric autoregressive model as is expounded in Section 7. 7 in some detail. Section 6. 6 discusses the related problem of fit ting a regression model, using a certain partial sum process. Inboth sections a certain transform of the underlying process is shown to provide asymptotically distribution free tests. Other important changes are as follows. Theorem 7. 3 |
| Physical Description: | 1 Online-Ressource (XVII, 425p) |
| ISBN: | 9781461300557 9780387954769 |
| ISSN: | 0930-0325 |
| DOI: | 10.1007/978-1-4613-0055-7 |
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| spelling | Koul, Hira L. Verfasser aut Weighted Empirical Processes in Dynamic Nonlinear Models by Hira L. Koul Second Edition New York, NY Springer New York 2002 1 Online-Ressource (XVII, 425p) txt rdacontent c rdamedia cr rdacarrier Lecture Notes in Statistics 166 0930-0325 The role of the weak convergence technique via weighted empirical processes has proved to be very useful in advancing the development of the asymptotic theory of the so called robust inference procedures corresponding to non-smooth score functions from linear models to nonlinear dynamic models in the 1990's. This monograph is an ex panded version of the monograph Weighted Empiricals and Linear Models, IMS Lecture Notes-Monograph, 21 published in 1992, that includes some aspects of this development. The new inclusions are as follows. Theorems 2. 2. 4 and 2. 2. 5 give an extension of the Theorem 2. 2. 3 (old Theorem 2. 2b. 1) to the unbounded random weights case. These results are found useful in Chapters 7 and 8 when dealing with ho moscedastic and conditionally heteroscedastic autoregressive models, actively researched family of dynamic models in time series analysis in the 1990's. The weak convergence results pertaining to the partial sum process given in Theorems 2. 2. 6 . and 2. 2. 7 are found useful in fitting a parametric autoregressive model as is expounded in Section 7. 7 in some detail. Section 6. 6 discusses the related problem of fit ting a regression model, using a certain partial sum process. Inboth sections a certain transform of the underlying process is shown to provide asymptotically distribution free tests. Other important changes are as follows. Theorem 7. 3 Statistics Mathematical statistics Statistical Theory and Methods Statistik Regressionsmodell (DE-588)4127980-3 gnd rswk-swf Autoregressiver Prozess (DE-588)4294677-3 gnd rswk-swf Autoregressiver Prozess (DE-588)4294677-3 s 1\p DE-604 Regressionsmodell (DE-588)4127980-3 s 2\p DE-604 https://doi.org/10.1007/978-1-4613-0055-7 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 |
| spellingShingle | Koul, Hira L. Weighted Empirical Processes in Dynamic Nonlinear Models Statistics Mathematical statistics Statistical Theory and Methods Statistik Regressionsmodell (DE-588)4127980-3 gnd Autoregressiver Prozess (DE-588)4294677-3 gnd |
| subject_GND | (DE-588)4127980-3 (DE-588)4294677-3 |
| title | Weighted Empirical Processes in Dynamic Nonlinear Models |
| title_auth | Weighted Empirical Processes in Dynamic Nonlinear Models |
| title_exact_search | Weighted Empirical Processes in Dynamic Nonlinear Models |
| title_full | Weighted Empirical Processes in Dynamic Nonlinear Models by Hira L. Koul |
| title_fullStr | Weighted Empirical Processes in Dynamic Nonlinear Models by Hira L. Koul |
| title_full_unstemmed | Weighted Empirical Processes in Dynamic Nonlinear Models by Hira L. Koul |
| title_short | Weighted Empirical Processes in Dynamic Nonlinear Models |
| title_sort | weighted empirical processes in dynamic nonlinear models |
| topic | Statistics Mathematical statistics Statistical Theory and Methods Statistik Regressionsmodell (DE-588)4127980-3 gnd Autoregressiver Prozess (DE-588)4294677-3 gnd |
| topic_facet | Statistics Mathematical statistics Statistical Theory and Methods Statistik Regressionsmodell Autoregressiver Prozess |
| url | https://doi.org/10.1007/978-1-4613-0055-7 |
| work_keys_str_mv | AT koulhiral weightedempiricalprocessesindynamicnonlinearmodels |