Bertail / Doukhan / Soulier Dependence in Probability and Statistics

1. Auflage 2006
ISBN: 978-0-387-36062-1
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 490 Seiten, Web PDF

Reihe: Lecture Notes in Statistics

This book gives a detailed account of recent developments in the field of probability and statistics for dependent data. It 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 section is devoted to statistical estimation problems and specific applications. The book is written as a succession of papers by field specialists, 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 book considers recent developments on weak dependent time series, including some new results for Markov chains, and fills a gap between the probability and statistical literature and the dynamical system literature. The book also presents new results on strong dependence with an emphasis on non-linear processes and random fields.

Zielgruppe

Research

Autoren/Hrsg.

Bertail, Patrice

Doukhan, Paul

Soulier, Philippe

Inhaltsverzeichnis

Weak dependence and related concepts.- Regeneration-based statistics for Harris recurrent Markov chains.- Subgeometric ergodicity of Markov chains.- Limit Theorems for Dependent U-statistics.- Recent results on weak dependence for causal sequences. Statistical applications to dynamical systems..- Parametrized Kantorovich-Rubinštein theorem and application to the coupling of random variables.- Exponential inequalities and estimation of conditional probabilities.- Martingale approximation of non adapted stochastic processes with nonlinear growth of variance.- Strong dependence.- Almost periodically correlated processes with long memory.- Long memory random fields.- Long Memory in Nonlinear Processes.- A LARCH(?) Vector Valued Process.- On a Szegö type limit theorem and the asymptotic theory of random sums, integrals and quadratic forms.- Aggregation of Doubly Stochastic Interactive Gaussian Processes and Toeplitz forms of U-Statistics.- Statistical Estimation and Applications.- On Efficient Inference in GARCH Processes.- Almost sure rate of convergence of maximum likelihood estimators for multidimensional diffusions.- Convergence rates for density estimators of weakly dependent time series.- Variograms for spatial max-stable random fields.- A non-stationary paradigm for the dynamics of multivariate financial returns.- Multivariate Non-Linear Regression with Applications.- Nonparametric estimator of a quantile function for the probability of event with repeated data.