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Weak Dependence: With Examples and Applications

  • Jérôme Dedecker
  • Paul Doukhan
  • Gabriel Lang
  • León R. José Rafael
  • Sana Louhichi
  • Clémentine Prieur

Part of the Lecture Notes in Statistics book series (LNS, volume 190)

Table of contents

  1. Front Matter
    Pages I-XIV
  2. Jérôme Dedecker, Paul Doukhan, Gabriel Lang, León R. José Rafael, Sana Louhichi, Clémentine Prieur
    Pages 1-8
  3. Jérôme Dedecker, Paul Doukhan, Gabriel Lang, León R. José Rafael, Sana Louhichi, Clémentine Prieur
    Pages 9-20
  4. Jérôme Dedecker, Paul Doukhan, Gabriel Lang, León R. José Rafael, Sana Louhichi, Clémentine Prieur
    Pages 21-65
  5. Jérôme Dedecker, Paul Doukhan, Gabriel Lang, León R. José Rafael, Sana Louhichi, Clémentine Prieur
    Pages 67-101
  6. Jérôme Dedecker, Paul Doukhan, Gabriel Lang, León R. José Rafael, Sana Louhichi, Clémentine Prieur
    Pages 103-134
  7. Jérôme Dedecker, Paul Doukhan, Gabriel Lang, León R. José Rafael, Sana Louhichi, Clémentine Prieur
    Pages 135-152
  8. Jérôme Dedecker, Paul Doukhan, Gabriel Lang, León R. José Rafael, Sana Louhichi, Clémentine Prieur
    Pages 153-197
  9. Jérôme Dedecker, Paul Doukhan, Gabriel Lang, León R. José Rafael, Sana Louhichi, Clémentine Prieur
    Pages 199-212
  10. Jérôme Dedecker, Paul Doukhan, Gabriel Lang, León R. José Rafael, Sana Louhichi, Clémentine Prieur
    Pages 213-221
  11. Jérôme Dedecker, Paul Doukhan, Gabriel Lang, León R. José Rafael, Sana Louhichi, Clémentine Prieur
    Pages 223-246
  12. Jérôme Dedecker, Paul Doukhan, Gabriel Lang, León R. José Rafael, Sana Louhichi, Clémentine Prieur
    Pages 247-264
  13. Jérôme Dedecker, Paul Doukhan, Gabriel Lang, León R. José Rafael, Sana Louhichi, Clémentine Prieur
    Pages 265-281
  14. Jérôme Dedecker, Paul Doukhan, Gabriel Lang, León R. José Rafael, Sana Louhichi, Clémentine Prieur
    Pages 283-303
  15. Back Matter
    Pages 305-318

About this book

Introduction

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.

Keywords

Resampling fitting parametric statistics statistics

Authors and affiliations

  • Jérôme Dedecker
    • 1
  • Paul Doukhan
    • 2
    • 3
  • Gabriel Lang
    • 4
  • León R. José Rafael
    • 5
  • Sana Louhichi
    • 6
  • Clémentine Prieur
    • 7
  1. 1.Laboratoire de Statistique, Théorique et AppliquéeUniversité Paris 675013 ParisFrance
  2. 2.ENSAE, Laboratoire de Statistique du CREST (Paris Tech)France
  3. 3.SAMOS-MATISSE (Statistique Appliquée et Modélisation Stochastique)Centre d’Economie de la Sorbonne Université Paris 1-Panthéon-Sorbonne CNRSFrance
  4. 4.Equipe MORSE UMR MIA518 INRAF-75005 ParisFrance
  5. 5.Escuela de MatematicaUniversidad Central de VenezuelaCaracas 1041-AVenezuela
  6. 6.Laboratoire de MathématiquesUniversité Paris-Sud–Bât 425France
  7. 7.Génie Mathématique et Modélisation, Laboratoire de Statistique et ProbabilitésINSA ToulouseFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-387-69952-3
  • Copyright Information Springer Science+Business Media, LLC 2007
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-69951-6
  • Online ISBN 978-0-387-69952-3
  • Series Print ISSN 0930-0325
  • Buy this book on publisher's site
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