Empirical Process Techniques for Dependent Data (eBook, PDF)

Redaktion: Dehling, Herold; Sörensen, Michael; Mikosch, Thomas

• Format: PDF

Produktbeschreibung

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,

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Produktdetails

• Verlag: Birkhäuser Boston
• Seitenzahl: 383
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9781461200994
• Artikelnr.: 44194379

Autorenporträt

Dehling, H. / Mikosch, T., both Universtity of Groningen, The Netherlands / Sörensen, M., University of Copenhagen, Denmark

Inhaltsangabe

I. A Tutorial on Empirical Process Techniques for Dependent Data.- Empirical Process Techniques for Dependent Data.- 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.- 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.- 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.

Rezensionen

"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