Extreme Value Theory: An Introduction

ISBN-13: 9780387239460 / Angielski / Twarda / 2006 / 442 str.

Laurens De Haan; Ana Ferreira

Opis

This treatment of extreme value theory is unique in book literature in that it focuses on some beautiful theoretical results along with applications. All the main topics covering the heart of the subject are introduced to the reader in a systematic fashion so that in the final chapter even the most recent developments in the theory can be understood. Key to the presentation is the concentration on the probabilistic and statistical aspects of extreme values without major emphasis on such related topics as regular variation, point processes, empirical distribution functions, and Brownian motion. The work is an excellent introduction to extreme value theory at the graduate level, requiring only some mathematical maturity.

Recenzje

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)

Spis treści

One-Dimensional Observations.- Limit Distributions and Domains of Attraction.- Extreme and Intermediate Order Statistics.- Estimation of the Extreme Value Index and Testing.- Extreme Quantile and Tail Estimation.- Advanced Topics.- Finite-Dimensional Observations.- Basic Theory.- Estimation of the Dependence Structure.- Estimation of the Probability of a Failure Set.- Observations That Are Stochastic Processes.- Basic Theory in C[0,1].- Estimation in C[0, 1].

Blurb

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.