Extremwertstatistik

Submitted by ruckdeschel on Mon, 01/31/2022 - 17:59
Person(s) in Charge
Prof. Dr. Peter Ruckdeschel
Topic
Statistics for extreme values and applications
Type
lecture (3) + exercise course (1)
KP
6KP
Workload
180h
Hours/Week
4.00h
Exam Type
oral exam
Access Limits
None
Prerequisites
builds up on basic courses in Statistics/Stochastics
Location
Uni Oldenburg, Mo 10:15-11:45 and Tu 08:15-9:45, both in W01 0 012
Description

Contents

  • Maxima:  the Generalized Extreme Value Distribution and its properties, Fisher-Tippet-Gnedenko-Thm /domains of attraction, block maxima
  • Peaks over threshold: the Generalized Pareto Distribution and its properties, Pickands-Balkema-deHaan Thm/domains of attraction, Hill-type estimators
  • Point processes: the Poisson Process; duality with the Exponential Distribution, relevance for extreme value theory
  • Diagnostics: Mean-Excess Plot, Return Level Plot, Extremal-Index

Goals/Competencies:

The students get to know the limit theorems of extreme value statistics and the related statistical methodology and can apply these techniques to real data in R; key R-packages will be ismev, gev, and RobExtremes all available on CRAN.

References

  • Coles, S., et al.: An introduction to statistical modeling of extreme values. Springer.
  • Embrechts, P, Klüppelberg, C., Mikosch, T.: Modelling extremal events: for insurance and finance. Springer.
  • McNeil, A.J., Frey, R., Embrechts, P. Quantitative risk management: concepts, techniques, and tools. Princeton university press.
  • Reiss, R-D., Thomas, M. Statistical analysis of extreme values. Birkhäuser
Semester