Extreme Value Theory An Introduction [Paperback]

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.

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].

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 valuelCé