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Birkhäuser

Parametric Statistical Change Point Analysis

  • Book
  • © 2000

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Table of contents (7 chapters)

Keywords

About this book

Recently there has been a keen interest in the statistical analysis of change point detec­ tion and estimation. Mainly, it is because change point problems can be encountered in many disciplines such as economics, finance, medicine, psychology, geology, litera­ ture, etc. , and even in our daily lives. From the statistical point of view, a change point is a place or time point such that the observations follow one distribution up to that point and follow another distribution after that point. Multiple change points problem can also be defined similarly. So the change point(s) problem is two fold: one is to de­ cide if there is any change (often viewed as a hypothesis testing problem), another is to locate the change point when there is a change present (often viewed as an estimation problem). The earliest change point study can be traced back to the 1950s. During the fol­ lowing period of some forty years, numerous articles have been published in various journals and proceedings. Many of them cover the topic of single change point in the means of a sequence of independently normally distributed random variables. Another popularly covered topic is a change point in regression models such as linear regres­ sion and autoregression. The methods used are mainly likelihood ratio, nonparametric, and Bayesian. Few authors also considered the change point problem in other model settings such as the gamma and exponential.

Reviews

"The book summarizes recent developments in parametric change-point analysis. The emphases are on the discussion of a variety of models and formation of test statistics based on three basic methods, namely, the generalized likelihood ratio test (GLRT), Bayesian and information criterion approaches. The main results focus on deriving asymptotically null distributions for the corresponding tests. A major contribution made by the authors is the use of an information criterion to form a test statistic. Another attractive feature is the application of different models to a variety of different data sets...Overall, the book gives a clear and systematic presentation of the models and methods. It will be an excellent source for theoretical and applied statisticians who are interested in research on change-point analysis and its applications to many areas."   —Mathematical Reviews

"This work is concerned with aposteriori methods of parametric statistical change point analysis...Illustrative examples and useful numerical tables are provided throughout the book."  â€”Zentralblatt MATH

"The statistical theory of change point analysis is now well developed, and the monograph under review represents a timely account of a part of it. The book contains detailed explanation of some technical papers on parametric change point analysis. Considerable effort is devoted to presenting detailed proofs of the asymptotic distributions of likelihood procedures based on test statistics for univariate and multivariate normal distributions. The book is generally aimed at researchers and graduate students with a good background in probability and asymptotic theory...In summary, the monograph under review is timely and a good starting point for both researchers and theoretically strong graduate students interested in pursuing theoretical research in nonsequential parametric single-path change pointproblems."   —SIAM Review

"Change point detection is of importance in engineering, economics, medicine, science and several fields. This book offers an in-depth study of the problem in some parametric models...The book partially relies on research papers written by the authors. For the reader's convenience, detailed calculations establishing the results are included. On the other hand, examples and statistical tables help the application-oriented reader. Statisticians in science, engineering and finance will find this book useful. It can be recommended also to students, both undergraduate and graduate."   —Publicationes Mathematicae

"In this monograph under review, the authors collect and describe a series of important models in change point analysis which have proved to be useful in statistical applications...The majority of change point procedures discussed here is for (univariate or multivariate) normal models. This is because such models are very popular and widely used in practice. But other parametric models, like the gamma, exponential, binomial or Poisson model, are also studied...[This] monograph can serve as a useful reference text for various purposes. The advanced student should be encouraged to do some own research work in an interesting area, the researcher will find a comprehensive exposition of recent developments, and the applied statistician will have a useful collection of change point methods and procedures, illustrated by many numerical examples of real data sets from different applications."   —Statistics & Decisions

Authors and Affiliations

  • Department of Mathematics and Statistics, University of Missouri-Kansas City, Kansas City, USA

    Jie Chen

  • Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, USA

    A. K. Gupta

Bibliographic Information

  • Book Title: Parametric Statistical Change Point Analysis

  • Authors: Jie Chen, A. K. Gupta

  • DOI: https://doi.org/10.1007/978-1-4757-3131-6

  • Publisher: Birkhäuser Boston, MA

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 2000

  • eBook ISBN: 978-1-4757-3131-6Published: 11 November 2013

  • Edition Number: 1

  • Number of Pages: VIII, 184

  • Topics: Statistical Theory and Methods

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