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Empirical Process Techniques for Dependent Data

  • Book
  • © 2002

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Editors:
  1. Herold Dehling

    1. Fakultät für Mathematik, Ruhr-Universität Bochum, Bochum, Germany

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  2. Thomas Mikosch

    1. Laboratory of Actuarial Mathematics, University of Copenhagen, Copenhagen, Denmark

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  3. Michael Sørensen

    1. Department of Statistics and Operations Research, University of Copenhagen, Copenhagen, Denmark

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Table of contents (14 chapters)

  1. Front Matter

    Pages i-xi
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  2. A Tutorial on Empirical Process Techniques for Dependent Data

    1. Front Matter

      Pages 1-1
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    2. Empirical Process Techniques for Dependent Data

      • Herold Dehling, Walter Philipp
      Pages 3-113

  3. Techniques for the Empirical Process of Stationary Sequences

    1. Front Matter

      Pages 115-115
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    2. Weak Dependence: Models and Applications

      • Patrick Ango Nze, Paul Doukhan
      Pages 117-136

    3. Maximal Inequalities and Empirical Central Limit Theorems

      • Jérôme Dedecker, Sana Louhichi
      Pages 137-159

    4. On Hoeffding’s Inequality for Dependent Random Variables

      • Sara A. van de Geer
      Pages 161-169

    5. On the Coupling of Dependent Random Variables and Applications

      • Florence Merlevède, Magda Peligrad
      Pages 171-193

    6. Empirical Processes of Residuals

      • István Berkes, Lajos Horváth
      Pages 195-209

  4. The Empirical Process of Long Range Dependent Processes

    1. Front Matter

      Pages 211-211
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    2. Asymptotic Expansion of the Empirical Process of Long Memory Moving Averages

      • Hira L. Koul, Donatas Surgailis
      Pages 213-239

    3. The Reduction Principle for the Empirical Process of a Long Memory Linear Process

      • Liudas Giraitis, Donatas Surgailis
      Pages 241-255

    4. Distributional Limit Theorems for Empirical Processes Generated by Functions of a Stationary Gaussian Process

      • Miguel A. Arcones
      Pages 257-271

  5. Empirical Spectral Process Techniques

    1. Front Matter

      Pages 273-273
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    2. Empirical Spectral Processes and Nonparametric Maximum Likelihood Estimation for Time Series

      • Rainer Dahlhaus, Wolfgang Polonik
      Pages 275-298

    3. Empirical Processes Techniques for the Spectral Estimation of Fractional Processes

      • Philippe Soulier
      Pages 299-321

  6. The Tail Empirical Process in Extreme Value Theory

    1. Front Matter

      Pages 323-323
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    2. Tail Empirical Processes Under Mixing Conditions

      • Holger Drees
      Pages 325-342

  7. Bootstrap Techniques

    1. Front Matter

      Pages 343-343
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    2. On the Bootstrap and Empirical Processes for Dependent Sequences

      • Dragan Radulović
      Pages 345-364
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Keywords

About this book

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,

Reviews

"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

Editors and Affiliations

  • Fakultät für Mathematik, Ruhr-Universität Bochum, Bochum, Germany

    Herold Dehling

  • Laboratory of Actuarial Mathematics, University of Copenhagen, Copenhagen, Denmark

    Thomas Mikosch

  • Department of Statistics and Operations Research, University of Copenhagen, Copenhagen, Denmark

    Michael Sørensen

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