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Instructors: Prof. Dr. Holger Drees
Event type:
Lecture
Displayed in timetable as:
M-VMS-V
Hours per week:
2
Language of instruction:
English
Min. | Max. participants:
- | -
Comments/contents:
Extreme random events play an important role in many fields. For instance, dams and storm water retention reservoirs must be designed such that they offer sufficient protection in case of extreme floods, storms or rainfall. Investors should try to quantify the risk of extreme losses, and for insurance companies the risk of extreme damages play a central role for natural hazard insurances, industrial fire insurances and other lines of business. In practice, questions of the following type arise: How high must a dike at the North Sea be built such that the risk of a flooding in a given year is at most 0.01%? What is the maximal daily loss from an investment which is not exceeded with a probability of at least 0.5%? Are there indications that the dependence between the gains and losses from different investments increases during a crash?
The models and methods used in classical statistics are often not appropriate to answer such questions. For example, in this context, the normal approximation widely used in classical statistics is usually very inaccurate, even if the central limit theorem applies.
In the lectures and the accompanying exercise group we will first discuss a systematic approach to model univariate (one-dimensional) extreme observations. Then methods for fitting these models to data and resulting estimators of quantities of interest (like extreme quantiles) are presented. Throughout the course we will also discuss real data sets and problems arising in their analysis.
Learning objectives:
You are expected to understand the specific challenges when analyzing extreme data and extreme risks. You should be able to apply basic techniques and methods for this analysis.
Didactic concept:
The content of this course will be presented in videos. In addition, detailed lecture notes will be provided. Questions concerning this material will be clarified during online consultation hours.
All material will be provided via the moodle course
https://lernen.min.uni-hamburg.de/course/view.php?id=1112
password: Pickands
For the understanding of the results and methods discussed in the lectures, it is necessary that you actively participate in the exercise sessions. In particular, you should use the opportunity to gain experience with problems arising when dealing with real data. To this end, in addition to real data also the program Xtremes will be provided that has been specifically designed for the analysis of extremes. Moreover, there are packages for extreme value analysis available for the statistical software R.
Literature:
In addition to the lecture notes you may find the following monographs helpful:
- Beirlant, J., Goegebeur, Y., Segers, J., and Teugels, J. (2004). Statistics of Extremes: Theory and Applications. Wiley.
- de Haan, L., and Ferreira, A. (2006). Extreme Value Theory: An Introduction. Springer.
- Resnick, S. (2007). Heavy-tail Phenomena: Probabilistic and Statistical Modeling. Springer.
Additional examination information:
In order to take part in the final oral exam, each participant has to score a minimum percentage of points in the homework sheets. Details will be given in moodle at the begin of the course.
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