# Empirical Process Techniques for Dependent Data

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August 2002

## Beschreibung

### Beschreibung

Empirical process techniques for independent data have been usedfor 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,

### Inhaltsverzeichnis

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

### Pressestimmen

"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

EAN: 9780817642013

ISBN: 0817642013

Untertitel: 2002. Auflage.
Sprache: Englisch.

Verlag: SPRINGER VERLAG GMBH

Erscheinungsdatum: August 2002

Seitenanzahl: 383 Seiten

Format: gebunden

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