Parametric Statistical Change Point Analysis

This work is an in-depth study of the change point problem from a general point of view and a further examination of change point analysis of the most commonly used statistical models. Change point problems are encountered in such disciplines as economics, finance, medicine, psychology, signal processing, and geology, to mention only several. The exposition is clear and systematic, with a great deal of introductory material included. Different models are presented in each chapter, including gamma and exponential models, rarely examined thus far in the literature. Other models covered in detail are the multivariate normal, univariate normal, regression, and discrete models. Extensive examples throughout the text emphasize key concepts and different methodologies are used, namely the likelihood ratio criterion, and the Bayesian and information criterion approaches. A comprehensive bibliography and two indices complete the study.

Table of Contents:
Preliminaries; univariate normal model; multivariate normal model; regression models; gamma model; exponential model; discrete models.

Review :
"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." --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 point problems." --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