Dependence in Probability and Statistics

  • Patrice Bertail
  • Philippe Soulier
  • Paul Doukhan

Part of the Lecture Notes in Statistics book series (LNS, volume 187)

Table of contents

  1. Front Matter
    Pages I-VIII
  2. Weak dependence and related concepts

  3. Strong dependence

    1. Front Matter
      Pages 157-157
    2. Anne Philippe, Donatas Surgailis, Marie-Claude Viano
      Pages 159-194
    3. Frédéric Lavancier
      Pages 195-220
    4. Rohit Deo, Mengchen Hsieh, Clifford M. Hurvich, Philippe Soulier
      Pages 221-244
    5. Paul Doukhan, Gilles Teyssière, Pablo Winant
      Pages 245-258
  4. Statistical Estimation and Applications

    1. Front Matter
      Pages 303-303
    2. Christian Francq, Jean-Michel Zakoïan
      Pages 305-327
    3. Nicolas Ragache, Olivier Wintenberger
      Pages 349-372
    4. Dan Cooley, Philippe Naveau, Paul Poncet
      Pages 373-390
    5. Stefano Herzel, Cătălin Stărică, Reha Tütüncüc
      Pages 391-429
    6. Tata Subba Rao, Gyorgy Terdik
      Pages 431-473
  5. Back Matter
    Pages 491-492

About this book


This book gives a detailed account of some recent developments in the field of probability and statistics for dependent data. The book covers a wide range of topics from Markov chain theory and weak dependence with an emphasis on some recent developments on dynamical systems, to strong dependence in times series and random fields. A special section is devoted to statistical estimation problems and specific applications. The book is written as a succession of papers by some specialists of the field, alternating general surveys, mostly at a level accessible to graduate students in probability and statistics, and more general research papers mainly suitable to researchers in the field.

The first part of the book considers some recent developments on weak dependent time series, including some new results for Markov chains as well as some developments on new notions of weak dependence. This part also intends to fill a gap between the probability and statistical literature and the dynamical system literature. The second part presents some new results on strong dependence with a special emphasis on non-linear processes and random fields currently encountered in applications. Finally, in the last part, some general estimation problems are investigated, ranging from rate of convergence of maximum likelihood estimators to efficient estimation in parametric or non-parametric time series models, with an emphasis on applications with non-stationary data.

Patrice Bertail is researcher in statistics at CREST-ENSAE, Malakoff and Professor of Statistics at the University-Paris X. Paul Doukhan is researcher in statistics at CREST-ENSAE, Malakoff and Professor of Statistics at the University of Cergy-Pontoise. Philippe Soulier is Professor of Statistics at the University-Paris X.


Estimator Gaussian process Likelihood Markov chain Martingal Martingale Random variable Rang Variance ergodicity linear regression statistics stochastic processes

Editors and affiliations

  • Patrice Bertail
    • 1
    • 2
  • Philippe Soulier
    • 2
  • Paul Doukhan
    • 1
    • 3
  1. 1.L-S Timbre J340CRESTParis Cedex 14France
  2. 2.Laboratoire MODAL’XUniversité Paris XNanterre CedexFrance
  3. 3.Université de Cergy-PontoiseCergy-Pontoise CedexFrance

Bibliographic information

  • DOI
  • Copyright Information Springer Science+Business Media, LLC 2006
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-31741-0
  • Online ISBN 978-0-387-36062-1
  • Series Print ISSN 0930-0325
  • Buy this book on publisher's site