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Weak dependence : with examples and applications
This monograph is aimed at developing Doukhan/Louhichi's (1999) idea to measure asymptotic independence of a random process. The authors propose various examples of models fitting such conditions such as stable Markov chains, dynamical systems or more complicated models, nonlinear, non-Markovia...
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| Auteurs principaux : | , , , , , |
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| Format : | Livre |
| Langue : | anglais |
| Titre complet : | Weak dependence : with examples and applications / Jérôme Dedecker, Paul Doukhan, Gabriel Lang ... [et al.] |
| Édition : | 1st ed. 2007. |
| Publié : |
New York, NY :
Springer New York
, [20..] Cham : Springer Nature |
| Collection : | Lecture notes in statistics (New York. Springer. Internet) ; 190 |
| Accès en ligne : |
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| Condition d'utilisation et de reproduction : | Conditions particulières de réutilisation pour les bénéficiaires des licences nationales : https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 |
| Contenu : | Weak dependence. Models. Tools for non causal cases. Tools for causal cases. Applications of strong laws of large numbers. Central Limit theorem. Donsker Principles. Law of the iterated logarithm (LIL). The Empirical process. Functional estimation. Spectral estimation. Econometric applications and resampling |
| Sujets : | |
| Documents associés : | Autre format:
Weak dependence Autre format: Weak Dependence: With Examples and Applications Autre format: Weak dependence |
| Résumé : | This monograph is aimed at developing Doukhan/Louhichi's (1999) idea to measure asymptotic independence of a random process. The authors propose various examples of models fitting such conditions such as stable Markov chains, dynamical systems or more complicated models, nonlinear, non-Markovian, and heteroskedastic models with infinite memory. Most of the commonly used stationary models fit their conditions. The simplicity of the conditions is also their strength. The main existing tools for an asymptotic theory are developed under weak dependence. They apply the theory to nonparametric statistics, spectral analysis, econometrics, and resampling. The level of generality makes those techniques quite robust with respect to the model. The limit theorems are sometimes sharp and always simple to apply. The theory (with proofs) is developed and the authors propose to fix the notation for future applications. A large number of research papers deals with the present ideas; the authors as well as numerous other investigators participated actively in the development of this theory. Several applications are still needed to develop a method of analysis for (nonlinear) times series and they provide here a strong basis for such studies. Jérôme Dedecker (associate professor Paris 6), Gabriel Lang (professor at Ecole Polytechnique, ENGREF Paris), Sana Louhichi (Paris 11, associate professor at Paris 2), and Clémentine Prieur (associate professor at INSA, Toulouse) are main contributors for the development of weak dependence. José Rafael León (Polar price, correspondent of the Bernoulli society for Latino-America) is professor at University Central of Venezuela and Paul Doukhan is professor at ENSAE (SAMOS-CES Paris 1 and Cergy Pontoise) and associate editor of Stochastic Processes and their Applications. His Mixing: Properties and Examples (Springer, 1994) is a main reference for the concurrent notion of mixing |
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| Notes : | L'impression du document génère 323 p. Contributeurs : León R. José Rafael, Sana Louhichi, Clémentine Prieur (auteurs) |
| Bibliographie : | Bibliogr. Index |
| ISBN : | 978-0-387-69952-3 |
| DOI : | 10.1007/978-0-387-69952-3 |