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Extreme Value Theory: An Introduction (Springer Series in Operations Research and Financial Enginee)by Laurens De Haan
Synopses & Reviews
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.
Focuses on theoretical results along with applications All the main topics covering the heart of the subject are introduced to the reader in a systematic fashion Concentration is on the probabilistic and statistical aspects of extreme values Excellent introduction to extreme value theory at the graduate level, requiring only some mathematical maturity
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.
Table of Contents
Preface.- Part I: 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.- More Advanced Topics.- Part II: Finite-Dimensional Observations.- Basic Theory.- Estimating the Dependence Structure.- Estimation of the Probability of a Failure Set.- Part III: Observations that are Stochastic Processes.- Basic Theory.- Examples.- Estimation.- Appendix A: Regular Variation (proofs).
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