401-3919-60L An Introduction to the Modelling of Extremes
|Semester||Spring Semester 2016|
|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-Tippett 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: |
 S.G. Coles (2001) An Introduction to Statistical Modeling of
Extreme Values. Springer.
 R.-D. Reiss and M. Thomas (1997) Statistical Analyis of
Extreme Values. Birkhaeuser.
At an intermediate level:
 J. Beirlant, Y. Goegebeur, J. Segers and J.L. Teugels (2004)
Statistics of Extremes: Theory and Applications, Wiley.
 P. Embrechts, C. Klueppelberg and T. Mikosch (1997)
Modelling Extremal Events for Insurance and Finance.
 S. I. Resnick (2007) Heavy-Tail Phenomena. Probabilistic and
Statistical Modeling. Springer.
At a more advanced level:
 L. de Haan and A. Ferreira (2006) Extreme Value Theory. An
 S. I. Resnick (1987) Extreme Values, Regular Variation,
and Point Processes. Springer.