Extremwertstatistik

Submitted by ruckdeschel on Mon, 06/18/2018 - 21:57
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 or written exam
Access Limits
None
Prerequisites
builds up on basic courses in Statistics/Stochastics
Location
Uni Oldenburg, Tu + Th, 16:00-18:00, at W01 0-006
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.

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