Empirical Process Techniques for Dependent Data

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Empirical Process Techniques for Dependent Data

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  • 製本 Hardcover:ハードカバー版／ページ数 381 p.
  • 言語 ENG
  • 商品コード 9780817642013
  • DDC分類 519.5

Full Description

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,

Contents

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.