Parametric Statistical Change Point Analysis: With Applications to Genetics, Medicine, and Finance

ISBN-13: 9780817648008 / Angielski / Twarda / 2011 / 288 str.

Jie Chen; Arjun K. Gupta

Opis

Overall, the book gives a clear and systematic presentation of 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 (Review of the First Edition)§Revised and expanded, Parametric Statistical Change Point Analysis, Second Edition is an in-depth study of the change point problem from a general point of view, and a deeper look at change point analysis of the most commonly used statistical models. For some time, change point problems have appeared throughout the sciences in such disciplines as economics, medicine, psychology, signal processing, and geology; more recently, they have also been found extensively in applications related to biomedical imaging data, array Comparative Genomic Hybridization (aCGH) data, and gene expression data. These areas of interest new and old have motivated substantial research on change point problems and led to a significant body of literature in the field. The present monograph stands as a valuable contribution to this literature. §Key features and topics: §Clear and systematic exposition with a great deal of introductory material included; §Different models in each chapter, including gamma and exponential models, rarely examined thus far in the literature; §Extensive examples to emphasize key concepts and different methodologies used, namely the likelihood ratio criterion as well as the Bayesian and information criterion approaches; §An up-to-date comprehensive bibliography and two indices.§New to the Second Edition: §New examples of change point analysis in modern molecular biology and other fields such as finance and air traffic control; §Two new sections of applications of the underlying change point models in analyzing the array Comparative Genomic Hybridization (aCGH) data for DNA copy number changes; §A new chapter on change points in the hazard function; §A new chapter on other practical change point models, such as the epidemic change point model and a smooth-and-abrupt change point model.§This monograph will be a highly useful resource for an impressively broad range of researchers in statistics, as well as a useful supplement for graduate courses in the field.

Recenzje

From the reviews of the second edition:

"The book summarizes several fundamental approaches in dealing with parametric change point models including likelihood, information criteria, and the Bayesian method. ... The book serves as an excellent graduate-level textbook for students in statistics, biostatistics, and econometrics, and is a must-read reference for researchers and practitioners on change point models." (Yanhong Wu, Mathematical Reviews, September, 2013)

"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 (Review of the First Edition)

"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 (Review of the First Edition)

"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 [a] 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 (Review of the First Edition)

"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 (Review of the First Edition)

"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 [of his] 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 (Review of the First Edition)

Spis treści

Preface.- Preliminaries.- Introduction.- Univariate Normal Model.- Multivariate Normal Model.- Regression Model.- Gamma Model.- Exponential Model.- Change Point Model for the Hazard Function.- Discrete Models.- Other Models.- Bibliography.- Author Index.- Subject Index.