Empirical Process Techniques for Dependent Data

ISBN-13: 9781461266112 / Angielski / Miękka / 2012 / 383 str.

Herold Dehling; Thomas Mikosch; Michael Sorensen

Opis

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.

Recenzje

"The book is an outgrowth of the workshop held in November 2000 at the University of Copenhagen.  It opens by an extensive tutorial covering the topic from the early roots up to recent developments and is accompanied by a vast bibliography of newly 150 items...

The book is the first comprehensive treatment of this topic, perhaps because only the present-day computers are able to meet the enormous requirements for high speed and large memory necessary for the application of statistical techniques to dependent data. It will be suitable for classroom use as well as for specialists in probability and statistics and for practitioners in the above mentioned branches of dependent data applications." ---APPLICATIONS OF MATHEMATICS

Spis treści

Part I: A Tutorial on Empirical Process Techniques for Dependent Data * Part II: Techniques for the Empirical Process of Stationary Sequences * Weak Dependence: Models and Applications * Maximal Inequalities and Empirical Central Limit Theorems * On Hoeffding's Inequality for Dependent Random Variables * On the Coupling of Dependent Random Variables and Applications * Empirical Processes of Residuals * Part III: The Empirical Process of Long-Range Dependent Processes * Asymptotic Expansion of the Empirical Process of Long Memory Moving Averages * The Reduction Principle for the Empirical Process of a Long Memory Linear Process * Distributional Limit Theorems for Empirical Processes Generated by Functions of a Stationary Gaussian Process * Part IV: Empirical Spectral Process Techniques * Empirical Spectral Processes and Nonparametric Maximum Likelihood Estimation for Time Series * Empirical Processes Techniques for the Spectral Estimation of Fractional Processes * V: The Tail Empirical Process in Extreme Value Theory * Tail Empirical Processes Under Mixing Conditions * VI: Bootstrap Techniques * On the Bootstrap and Empirical Processes for Dependent Sequences * Frequency Domain Bootstrap for Time Series

O autorze

Empirical process techniques for independent data have been used for
many years in statistics and probability theory. This work gives an
introduction to a new theory of empirical process techniques ---
treating dependent data --- which has so far been scattered widely in
the statistical and probabilistic literature, and surveys the most
recent developments in various related fields. 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.