Jérome Dedecker, Paul Doukhan, Gabriel Lang, José Rafael Leon, Sana Louhichi, Clémentine Prieur

Weak Dependence: With Examples and Applications (eBook, PDF)

• Format: PDF

Produktbeschreibung

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 theconcurrent notion of mixing.

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Produktdetails

• Verlag: Springer US
• Seitenzahl: 322
• Erscheinungstermin: 29. Juli 2007
• Englisch
• ISBN-13: 9780387699523
• Artikelnr.: 37287942

Autorenporträt

Jérôme Dedecker, Unversity of Paris, France / Paul Doukhan, CREST, Malakoff, France / Gabriel Lang, ParisTech, Paris, France / José Rafael Leon, Universidad Central de Venezuela, Caracas, Venezuela / Sana Louhichi, University Paris-Sud, Orsay, France / Clémentine Prieur, INSA Toulouse, France

Inhaltsangabe

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.

Rezensionen

From the reviews:

"I appreciate this book as a very welcome and thorough discussion of the actual state-of-the art in the modeling of dependence structures. It provides a large number of motivating examples and applications, rigorous proofs, and valuable intuitions for the willing and mathematically well-trained reader with essential prior knowledge of the mathematical prerequisites of weak dependence ... . It is ... the book to those researchers already aware of the necessity of the methods discussed here." (Harry Haupt, Advances in Statistical Analysis, Vol. 93, 2009)

"This book ... provides a detailed description of the notion of weak dependence as well as properties and applications. ... Overall the book is neatly written ... . the book is very rich in its material as it contains earlier works on dependence and ... show a lot of applications of the theory. It also contains a large number of examples and expositions of the idea of weak dependence in models ... which provide good insight." (Dimitris Karlis, Zentralblatt MATH, Vol. 1165, 2009)