Gaussian and Non-Gaussian Linear Time Series and Random Fields:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
2000
|
| Schriftenreihe: | Springer Series in Statistics
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Much of this book is concerned with autoregressive and moving average linear stationary sequences and random fields. These models are part of the classical literature in time series analysis, particularly in the Gaussian case. There is a large literature on probabilistic and statistical aspects of these models- to a great extent in the Gaussian context. In the Gaussian case best predictors are linear and there is an extensive study of the asymptotics of asymptotically optimal estimators. Some discussion of these classical results is given to provide a contrast with what may occur in the non-Gaussian case. There the prediction problem may be nonlinear and problems of estimation can have a certain complexity due to the richer structure that non-Gaussian models may have. Gaussian stationary sequences have a reversible probability structure, that is, the probability structure with time increasing in the usual manner is the same as that with time reversed. Chapter 1 considers the question of reversibility for linear stationary sequences and gives necessary and sufficient conditions for the reversibility. A neat result of Breidt and Davis on reversibility is presented. A simple but elegant result of Cheng is also given that specifies conditions for the identifiability of the filter coefficients that specify a linear non-Gaussian random field |
| Beschreibung: | 1 Online-Ressource (XIII, 247 p) |
| ISBN: | 9781461212621 9781461270676 |
| ISSN: | 0172-7397 |
| DOI: | 10.1007/978-1-4612-1262-1 |
Internformat
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Datensatz im Suchindex
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| author | Rosenblatt, Murray |
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| author_sort | Rosenblatt, Murray |
| author_variant | m r mr |
| building | Verbundindex |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-1262-1 |
| format | Electronic eBook |
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| id | DE-604.BV042419789 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:05Z |
| institution | BVB |
| isbn | 9781461212621 9781461270676 |
| issn | 0172-7397 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027855206 |
| oclc_num | 1184433597 |
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| physical | 1 Online-Ressource (XIII, 247 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 2000 |
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| publisher | Springer New York |
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| spelling | Rosenblatt, Murray Verfasser aut Gaussian and Non-Gaussian Linear Time Series and Random Fields by Murray Rosenblatt New York, NY Springer New York 2000 1 Online-Ressource (XIII, 247 p) txt rdacontent c rdamedia cr rdacarrier Springer Series in Statistics 0172-7397 Much of this book is concerned with autoregressive and moving average linear stationary sequences and random fields. These models are part of the classical literature in time series analysis, particularly in the Gaussian case. There is a large literature on probabilistic and statistical aspects of these models- to a great extent in the Gaussian context. In the Gaussian case best predictors are linear and there is an extensive study of the asymptotics of asymptotically optimal estimators. Some discussion of these classical results is given to provide a contrast with what may occur in the non-Gaussian case. There the prediction problem may be nonlinear and problems of estimation can have a certain complexity due to the richer structure that non-Gaussian models may have. Gaussian stationary sequences have a reversible probability structure, that is, the probability structure with time increasing in the usual manner is the same as that with time reversed. Chapter 1 considers the question of reversibility for linear stationary sequences and gives necessary and sufficient conditions for the reversibility. A neat result of Breidt and Davis on reversibility is presented. A simple but elegant result of Cheng is also given that specifies conditions for the identifiability of the filter coefficients that specify a linear non-Gaussian random field Statistics Distribution (Probability theory) Mathematical statistics Statistical Theory and Methods Probability Theory and Stochastic Processes Statistik Lineares System (DE-588)4125617-7 gnd rswk-swf Gauß-Prozess (DE-588)4156111-9 gnd rswk-swf Zufälliges Feld (DE-588)4191094-1 gnd rswk-swf Zeitreihe (DE-588)4127298-5 gnd rswk-swf Zeitreihenanalyse (DE-588)4067486-1 gnd rswk-swf Zeitreihenanalyse (DE-588)4067486-1 s Zufälliges Feld (DE-588)4191094-1 s Gauß-Prozess (DE-588)4156111-9 s 1\p DE-604 Zeitreihe (DE-588)4127298-5 s Lineares System (DE-588)4125617-7 s 2\p DE-604 https://doi.org/10.1007/978-1-4612-1262-1 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 | Rosenblatt, Murray Gaussian and Non-Gaussian Linear Time Series and Random Fields Statistics Distribution (Probability theory) Mathematical statistics Statistical Theory and Methods Probability Theory and Stochastic Processes Statistik Lineares System (DE-588)4125617-7 gnd Gauß-Prozess (DE-588)4156111-9 gnd Zufälliges Feld (DE-588)4191094-1 gnd Zeitreihe (DE-588)4127298-5 gnd Zeitreihenanalyse (DE-588)4067486-1 gnd |
| subject_GND | (DE-588)4125617-7 (DE-588)4156111-9 (DE-588)4191094-1 (DE-588)4127298-5 (DE-588)4067486-1 |
| title | Gaussian and Non-Gaussian Linear Time Series and Random Fields |
| title_auth | Gaussian and Non-Gaussian Linear Time Series and Random Fields |
| title_exact_search | Gaussian and Non-Gaussian Linear Time Series and Random Fields |
| title_full | Gaussian and Non-Gaussian Linear Time Series and Random Fields by Murray Rosenblatt |
| title_fullStr | Gaussian and Non-Gaussian Linear Time Series and Random Fields by Murray Rosenblatt |
| title_full_unstemmed | Gaussian and Non-Gaussian Linear Time Series and Random Fields by Murray Rosenblatt |
| title_short | Gaussian and Non-Gaussian Linear Time Series and Random Fields |
| title_sort | gaussian and non gaussian linear time series and random fields |
| topic | Statistics Distribution (Probability theory) Mathematical statistics Statistical Theory and Methods Probability Theory and Stochastic Processes Statistik Lineares System (DE-588)4125617-7 gnd Gauß-Prozess (DE-588)4156111-9 gnd Zufälliges Feld (DE-588)4191094-1 gnd Zeitreihe (DE-588)4127298-5 gnd Zeitreihenanalyse (DE-588)4067486-1 gnd |
| topic_facet | Statistics Distribution (Probability theory) Mathematical statistics Statistical Theory and Methods Probability Theory and Stochastic Processes Statistik Lineares System Gauß-Prozess Zufälliges Feld Zeitreihe Zeitreihenanalyse |
| url | https://doi.org/10.1007/978-1-4612-1262-1 |
| work_keys_str_mv | AT rosenblattmurray gaussianandnongaussianlineartimeseriesandrandomfields |