Dependence in Probability and Statistics

1. Front Matter

   Pages I-VIII

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2. Weak dependence and related concepts

   1. Front Matter

      Pages 1-1

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   2. Regeneration-based statistics for Harris recurrent Markov chains

      • Patrice Bertail, Stéphan Clémençon

      Pages 3-54

   3. Subgeometric ergodicity of Markov chains

      • Randal Douc, Eric Moulines, Philippe Soulier

      Pages 55-64

   4. Limit Theorems for Dependent U-statistics

      • Herold Dehling

      Pages 65-86

   5. Recent results on weak dependence for causal sequences. Statistical applications to dynamical systems.

      • Clémentine Prieur

      Pages 87-104

   6. Parametrized Kantorovich-Rubinštein theorem and application to the coupling of random variables

      • Jérôme Dedecker, Clémentine Prieur, Paul Raynaud De Fitte

      Pages 105-121

   7. Exponential inequalities and estimation of conditional probabilities

      • V. Maume-Deschamps

      Pages 123-140

   8. Martingale approximation of non adapted stochastic processes with nonlinear growth of variance

      • Dalibor Volný

      Pages 141-156

3. Strong dependence

   1. Front Matter

      Pages 157-157

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   2. Almost periodically correlated processes with long memory

      • Anne Philippe, Donatas Surgailis, Marie-Claude Viano

      Pages 159-194

   3. Long memory random fields

      • Frédéric Lavancier

      Pages 195-220

   4. Long Memory in Nonlinear Processes

      • Rohit Deo, Mengchen Hsieh, Clifford M. Hurvich, Philippe Soulier

      Pages 221-244

   5. A LARCH(∞) Vector Valued Process

      • Paul Doukhan, Gilles Teyssière, Pablo Winant

      Pages 245-258

   6. On a Szegö type limit theorem and the asymptotic theory of random sums, integrals and quadratic forms

      • Florin Avram, Murad S. Taqqu

      Pages 259-286

   7. Aggregation of Doubly Stochastic Interactive Gaussian Processes and Toeplitz forms of U-Statistics

      • Didier Dacunha-Castelle, Lisandro Fermín

      Pages 287-302

4. Statistical Estimation and Applications

   1. Front Matter

      Pages 303-303

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   2. On Efficient Inference in GARCH Processes

      • Christian Francq, Jean-Michel Zakoïan

      Pages 305-327

   3. Almost sure rate of convergence of maximum likelihood estimators for multidimensional diffusions

      • Dasha Loukianova, Oleg Loukianov

      Pages 329-347

   4. Convergence rates for density estimators of weakly dependent time series

      • Nicolas Ragache, Olivier Wintenberger

      Pages 349-372

The purpose of this book is to give a detailed account of some recent devel- ments in the ?eld of probability and statistics for dependent data. It covers a wide range of topics from Markov chains theory, weak dependence, dynamical system to strong dependence and their applications. The title of this book has been somehow borrowed from the book ”Dependence in Probability and Statistics: a Survey of Recent Result” edited by Ernst Eberlein and Murad S. Taqqu, Birkh¨ auser (1986), which could serve as an excellent prerequisite for reading this book. We hope that the reader will ?nd it as useful and stimulating as the previous one. This book was planned during a conference, entitled “STATDEP2005: Statistics for dependent data”, organized by the Statistical Laboratory of the CREST (Research Center in Economy and Statistics), in Paris/Malako?, under the auspices of the French State Statistical Institute, INSEE. See http://www.crest.fr/pageperso/statdep2005/home.htm for some r- rospective informations. However this book is not a conference proceeding. This conference has witnessed the rapid growth of contributions on dep- dent data in the probabilistic and statistical literature and the need for a book covering recent developments scattered in various probability and s- tistical journals. To achieve such a goal, we have solicited some participants of the conferences as well as other specialists of the ?eld.

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

• L-S Timbre J340, CREST, Paris Cedex 14, France

  Patrice Bertail, Paul Doukhan

• Laboratoire MODAL’X, Université Paris X, Nanterre Cedex, France

  Patrice Bertail, Philippe Soulier

• Université de Cergy-Pontoise, Cergy-Pontoise Cedex, France

  Paul Doukhan

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