Empirical Process Techniques for Dependent Data

by Dehling, Herold; Mikosch, Thomas; Srensen, Michael

• ISBN13: 9780817642013
• ISBN10: 0817642013
• Format: Hardcover
• Copyright: 2002-09-01
• Publisher: Birkhauser

Summary

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.

Table of Contents

Preface	vii
I. A Tutorial on Empirical Process Techniques for Dependent Data	1	(114)
Empirical Process Techniques for Dependent Data	3	(112)
Herold Dehling
Walter Philipp
II. Techniques for the Empirical Process of Stationary Sequences	115	(96)
Weak Dependence: Models and Applications	117	(20)
Patrick Ango Nze
Paul Doukhan
Maximal Inequalities and Empirical Central Limit Theorems	137	(24)
Jerome Dedecker
Sana Louhichi
On Hoeffding's Inequality for Dependent Random Variables	161	(10)
Sara A. van de Geer
On the Coupling of Dependent Random Variables and Applications	171	(24)
Florence Merlevede
Magda Peligrad
Empirical Processes of Residuals	195	(16)
Istvan Berkes
Lajos Horvath
III. The Empirical Process of Long Range Dependent Processes	211	(62)
Asymptotic Expansion of the Empirical Process of Long Memory Moving Averages	213	(28)
Hira L. Koul
Donatas Surgailis
The Reduction Principle for the Empirical Process of a Long Memory Linear Process	241	(16)
Liudas Giraitis
Donatas Surgailis
Distributional Limit Theorems for Empirical Processes Generated by Functions of a Stationary Gaussian Process	257	(16)
Miguel A. Arcones
IV. Empirical Spectral Process Techniques	273	(50)
Empirical Spectral Processes and Nonparametric Maximum Likelihood Estimation for Time Series	275	(24)
Rainer Dahlhaus
Wolfgang Polonik
Empirical Processes Techniques for the Spectral Estimation of Fractional Processes	299	(24)
Philippe Soulier
V. The Tail Empirical Process in Extreme Value Theory	323	(20)
Tail Empirical Processes Under Mixing Conditions	325	(18)
Holger Drees
VI. Bootstrap Techniques	343	(22)
On the Bootstrap and Empirical Processes for Dependent Sequences	345	(20)
Dragan Radulovic
Frequency Domain Bootstrap for Time Series	365
Efstathios Paparoditis