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

Semester Frühjahrssemester 2014
Dozierende P. Embrechts
Periodizität jährlich wiederkehrende Veranstaltung
Lehrsprache Englisch

Kurzbeschreibung 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.
Lernziel 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.
Inhalt - 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
Skript There will be no script available.
Literatur 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.
[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.