Empirical process techniques for independent data have been used for many years in statistics and probability theory. These techniques have proved very useful for studying asymptotic properties of parametric as well as non-parametric statistical procedures. Recently, the need to model the dependence structure in data sets from many different subject areas such as finance, insurance, and telecommunications has led to new developments concerning the empirical distribution function and the empirical process for dependent, mostly stationary sequences. This work gives an introduction to this new theory of empirical process techniques, which has so far been scattered in the statistical and probabilistic literature, and surveys the most recent developments in various related fields. Key features: A thorough and comprehensive introduction to the existing theory of empirical process techniques for dependent data \* Accessible surveys by leading experts of the most recent developments in various related fields \* Examines empirical process techniques for dependent data, useful for studying parametric and non-parametric statistical procedures \* Comprehensive bibliographies \* An overview of applications in various fields related to empirical processes: e.g., spectral analysis of time-series, the bootstrap for stationary sequences, extreme value theory, and the empirical process for mixing dependent observations, including the case of strong dependence. To date this book is the only comprehensive treatment of the topic in book literature. It is an ideal introductory text that will serve as a reference or resource for classroom use in the areas of statistics, time-series analysis, extreme value theory, point process theory, and applied probability theory. Contributors: P. Ango Nze, M.A. Arcones, I. Berkes, R. Dahlhaus, J. Dedecker, H.G. Dehling, Front Matter....Pages i-xi Front Matter....Pages 1-1 Empirical Process Techniques for Dependent Data....Pages 3-113 Front Matter....Pages 115-115 Weak Dependence: Models and Applications....Pages 117-136 Maximal Inequalities and Empirical Central Limit Theorems....Pages 137-159 On Hoeffding’s Inequality for Dependent Random Variables....Pages 161-169 On the Coupling of Dependent Random Variables and Applications....Pages 171-193 Empirical Processes of Residuals....Pages 195-209 Front Matter....Pages 211-211 Asymptotic Expansion of the Empirical Process of Long Memory Moving Averages....Pages 213-239 The Reduction Principle for the Empirical Process of a Long Memory Linear Process....Pages 241-255 Distributional Limit Theorems for Empirical Processes Generated by Functions of a Stationary Gaussian Process....Pages 257-271 Front Matter....Pages 273-273 Empirical Spectral Processes and Nonparametric Maximum Likelihood Estimation for Time Series....Pages 275-298 Empirical Processes Techniques for the Spectral Estimation of Fractional Processes....Pages 299-321 Front Matter....Pages 323-323 Tail Empirical Processes Under Mixing Conditions....Pages 325-342 Front Matter....Pages 343-343 On the Bootstrap and Empirical Processes for Dependent Sequences....Pages 345-364 Frequency Domain Bootstrap for Time Series....Pages 365-381 Back Matter....Pages 383-383 This book contains accessible surveys by several leading experts in the field. The first part is a thorough and comprehensive introduction to the existing theory of empirical process techniques for dependent data, starting from the classical contributions of Billingsley and including present day research. The bibliography provides an excellent basis for further studies. The remaining parts of the book give an overview of the most recent applications in various fields related to empirical processes such as spectral analysis of time series, the bootstrap for stationary sequences, extreme value theory, and the empirical process for mixing dependent observations, including the case of strong dependence. This book is an ideal introductory text that will serve as a reference or resource for classroom use in the areas of statistics, time series analysis, extreme value theory, point process theory, and applied probability theory, analysis, extreme value theory, point process theory, and applied probability theory.
