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Extreme Value Theory: An Introduction (Springer Series in Operations Research) 2006th Edition

4.5 out of 5 stars 2 customer reviews
ISBN-13: 978-0387239460
ISBN-10: 0387239464
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Editorial Reviews

Review

From the reviews:

"According to the authors, who have provided significant contributions to this field by themselves, the ‘aim of this book is to give a thorough account of the basic theory of extreme values, probabilistic and statistical, theoretical and applied’. This goal has been certainly achieved. … The book certainly provides a nice ‘introduction’ into the recent developments of statistical (and probabilistic) extreme value theory. It will serve as a useful reference for all graduate students and researchers in the field." (Josef Steinebach, Zentralblatt MATH, Vol. 1101 (3), 2007)

"This book deals with the mature topic of extreme value theory (EVT) and its applications to diverse areas, including finance, and many others. … The authors are among the leading experts in the field of EVT and have written an authoritative treatment of the subject. It is an excellent reference book that also can be used as a textbook for an advanced special topics course on EVT. Practitioners interested in developing a deeper understanding of the area would benefit greatly from this text." (George Michailidis and Stilian Stoev, Technometrics, Vol. 49 (4), 2007)

"The book under review gives a solid overview of EVT including not only the probabilistic fundamentals but also the corresponding statistical theory. … the book also provides approximately 100 exercises and 100 references. The exercises should be considered as supplementary materials, since most of them are also important results in EVT literature. … can be highly recommended to anyone who is interested in the recent development of EVT theory and its statistical applications." (C. Zhou, Kwantitatieve Methoden, December, 2007)

"This book is in the long tradition of study of extreme value theory … . Two main themes are given full treatment here for the first time in textbook form. … This is a valuable feature of this book … . This book is a ‘must have’ for experts in extreme value theory, and would be an excellent choice for a special topics course on the probabilistic and theoretical sides of extreme value theory, especially a course emphasizing the multivariate aspects of extremes." (Jon A. Wellner, SIAM Review, Vol. 49 (2), 2007)

"This book is a recent addition to the Springer series on operations research and financial engineering. … The book is divided into three parts … . for someone wanting to work in statistical aspects of extreme value theory, the book is an excellent choice for self-study. The reader not only will receive a rigorous introduction, but also will get to the cutting edge of inference for extreme values." (Peter C. Kiessler, Journal of the American Statistical Association, Vol. 103 (482), 2008)

From the Back Cover

Extreme Value Theory offers a careful, coherent exposition of the subject starting from the probabilistic and mathematical foundations and proceeding to the statistical theory. The book covers both the classical one-dimensional case as well as finite- and infinite-dimensional settings. All the main topics at the heart of the subject are introduced in a systematic fashion so that in the final chapter even the most recent developments in the theory can be understood. The treatment is geared toward applications.

The presentation concentrates on the probabilistic and statistical aspects of extreme values such as limiting results, domains of attraction and development of estimators without emphasizing related topics such as point processes, empirical distribution functions and Brownian motion. An appendix on regular variation has been added since some required results in that area are not available in book form. The usefulness of the statistical theory is shown by treating several case studies in detail.

The book is a thorough, accessible, self-contained, graduate level treatment of modern extreme value theory and some of its applications. It is aimed at graduate students and researchers and requires only maturity in mathematics and statistics.

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Product Details

  • Hardcover: 418 pages
  • Publisher: Springer; 2006 edition (June 21, 2006)
  • Language: English
  • ISBN-10: 0387239464
  • ISBN-13: 978-0387239460
  • Product Dimensions: 6.1 x 1 x 9.2 inches
  • Shipping Weight: 1.6 pounds (View shipping rates and policies)
  • Average Customer Review: 4.5 out of 5 stars  See all reviews (2 customer reviews)
  • Amazon Best Sellers Rank: #536,480 in Books (See Top 100 in Books)

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By Michael R. Chernick on June 8, 2008
Format: Kindle Edition
In 1978 I got my PhD in statistics and did my dissertation on extreme value limit theorems for observations coming from stationary stochastic processes. At that time there were just two books that dealt with the theory and applications and the emphasis was on theory. Those were Gumbel's book published in 1960 and Galambos' that came out in 1978 just as I was finishing up my work. I was interested in both the theory and the applications. The Stanford University Statistics Department was funded to study the statistical analysis of air pollution data.

The data had both serial and spatial correlation structures. The issue was whether or not it was likely that levels of particular pollutants pollutants would soon or ever exceed the EPA emission limits. To answer the question correctly one needs to estimate or predict the maximum of a sequence of measurements and determine when it will cross a given level. The classical theory from Gumbel, Fisher and Tippets and Gnedenko dealt with independent observations. In the early 1970s Leadbetter, Loynes and others were extending the theory to stationary processes. It was clear that the solution to our problem required probability theory that was only starting to develop. In 1983 Leadbetter, Lindgren and Rootzen produced the first book to cover the theory and some applications for stationary processes and sequences.

The theory continued to develop over the nest 3 decades (I did not stay heavily involved in it) and in recent years with encouragement from a conference sponsored by the National Institute of Science and Technology the development of applications has grown. The last 5 years has seen a wealth of good books both applied and theoretical.
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Format: Hardcover
Initially, the problem seems intractable. How to understand a probability distribution with a long tail of possible values? Where this is little or no observed data at these large values. This probably stymied any serious research into this field until recent decades. The book discusses what can be deduced about such distributions, based on known observations at small values.

It is an advanced statistical monograph. Perhaps best suited for at least the graduate level. It differs qualitatively from most texts, but uses standard ideas like the maximum likelihood estimation, and moment estimators.

As to the applications of this book, that is also speculative. It is hoped that in fields like finance, the ideas can be used to posit more realistic models of rare but potentially catatrophic events.
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