Herold Dehling - Böcker

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.

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,

Dieses Buch gibt eine systematische Einführung in die grundlegenden Ideen und Konzepte der Wahrscheinlichkeitsrechnung. Die Darstellung ist elementar, d.h. ohne maßtheoretische Hilfsmittel und unter Verzicht auf größtmögliche Allgemeinheit. Der Weckung eines intuitiven Verständnisses wird im Zweifelsfall der Vorzug vor mathematischer Strenge gegeben. Die wesentlichen Begriffe und Resultate werden zunächst für diskrete Experimente eingeführt, und dabei stets an Beispielen illustriert. Im zweiten Teil des Buches stehen dichte-verteilte Zufallsvariablen im Mittelpunkt. Dabei werden u.a. die wichtigsten Verteilungen der parametrischen Statistik eingeführt und die wesentlichen Rechentechniken behandelt.Für die zweite Auflage wurde ein Kapitel über die Grundbegriffe der Testtheorie hinzugefügt.