Dependence in Probability and Statistics

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.

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.