401-3919-60L  An Introduction to the Modelling of Extremes

Semester Spring Semester 2013
Lecturers P. Embrechts
Periodicity yearly course
Language of instruction English


Abstract This course yields an introduction into the one-dimensional theory of extremes, and this both from a probabilistic as well as statistical point of view. This course can be seen as a first course on extremes, a sequel concentrating more on multivariate extremes.
Objective In this course, students learn to distinguish between so-called normal models, i.e. models based on the normal or Gaussian distribution, and so-called heavy-tailed or power-tail models.
They learn to do some standard modelling and data analysis for one-dimensional data. The probabilistic key theorems are the Fisher-Tipett Theorem and the Balkema-de Haan-Pickands Theorem. These lead to the statistical techniques for the analysis of extremes or rare events known as the Block Method, and Peaks Over Threshold method, respectively.
Content - Introduction to rare or extreme events
- Regular Variation
- The Convergence to Types Theorem
- The Fisher-Tippett Theorem
- The Method of Block Maxima
- The Maximal Domain of Attraction
- The Fre'chet, Gumbel and Weibull distributions
- The POT method
- The Point Process Method: a first introduction
- The Pickands-Balkema-de Haan Theorem and its applications
- Some extensions and outlook
Lecture notes There will be no script available.
Literature At a more elementary level:
[1] S.G. Coles (2001) An Introduction to Statistical Modeling of
Extreme Values. Springer.
[2] R.-D. Reiss and M. Thomas (1997) Statistical Analyis of
Extreme Values. Birkhaeuser.
At an intermediate level:
[3] J. Beirlant, Y. Goegebeur, J. Segers and J.L. Teugels (2004)
Statistics of Extremes: Theory and Applications, Wiley.
[4] P. Embrechts, C. Klueppelberg and T. Mikosch (1997)
Modelling Extremal Events for Insurance and Finance.
Springer.
[5] S. I. Resnick (2007) Heavy-Tail Phenomena. Probabilistic and
Statistical Modeling. Springer.
At a more advanced level:
[6] L. de Haan and A. Ferreira (2006) Extreme Value Theory. An
Introduction. Springer.
[7] S. I. Resnick (1987) Extreme Values, Regular Variation,
and Point Processes. Springer.
Prerequisites / Notice The course will be taught by Prof. Natalia Nolde.