Empirical Process Techniques for Dependent Data

Empirical process techniques have been used for many years in statistics and probability theory. In the recent past, the need to model dependence in real-life data sets has led to new developments for the empirical distribution function and the empirical process for dependent, mostly stationary sequences. Some work has been motivated by the classical results for {\ it independent} data and has been aimed at deriving similar results for stationary sequences. While the theory for {\ it dependent} data is well understood, no comprehensive text exists to date on the subject. The book is divided into two parts: Part I focuses on a thorough introduction to the existing theory of empirical process techniques for dependent data, starting from the classical contributions of Billingsley to present day research. Part II provides an overview of the most recent applications in various fields related to empirical processes, e.g., spectral analysis of time series, the bootstrap for stationary sequences, and the empirical process for mixing dependent observations, including the case of strong dependence. Top specialists contributing to the volume are: S.I. Resnick, H. Drees, R.A. Davis, T. Hsing, M. Arcones, E. Rio, P. Doukhan, L. Horvath, L. Giraitis, D. Surgailis, R. Dahlhaus, P. Soulier, R.V. Sachs, H.-R. Kunsch, P. Buhlmann, M. Peligrad, H. Dehling, Philipp To date this book is the only comprehensive treatment of the topic in the literature. It 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.