Extreme value theory
BMETE95MM16
2023/24. 2nd semester
Classes: Mon 14.15-15.45 H507
Evaluation
Points can be collected by:
- Homeworks (20%): there are three homework assignments during the semester with three exercises each. Each exercise is worth 3 points, 27 points can be collected in total. No minimal requirement. Problems and dealines see below.
- Midterm test (40%): 15th Apr 14.15-15.45 H507, 5 problems for 10 points each. Minimal requirement is 40% of 40 points = 16 points. Mainly exercises from the given list or similar and some basic questions in the theoretical part.
- Oral exam or short talk (40%): Oral exam about theory with proofs or 30 minutes short talk on a paper given by the istructor. 40 points can be collected, no minimal requirement.
The final mark is given based on a score between 0 and 100.
Grading scale: A final score between 40 and 54 yields a mark 2, between 55 and 69 is 3, between 70 and 84 is 4 and anything more than 85 is 5.
Exercises
Papers for short talk, deadline for signing up: 8th Apr
schedule of talks
Suggestions for short talks:
Each presentation takes 25-30 minutes including questions.
It is important to explain the concept of the paper without going into technical details.
Most papers cannot be fully explained in 30 minutes, and it is not required.
It is much more important to be understandable.
It is suggested to explain the model considered in the paper and to state the main results already in the first part of the talk.
Then further expanations, methods and proof ideas can follow depending on the topic and the paper.
Great talks can be given by using an overhead projector and slides as well as on the blackboard, neither of the two ways is preferred in principle.
When showing data and plots, slides might be more useful but mixed solutions are also possible.
Please attend each others presentations.
Hand-written lecture notes
- Domains of attraction for sums, stable laws
- Limit laws for normalized maxima, max-stable laws
- Fisher-Tippett theorem
- Maximum domains of attraction
- Generalized extreme value (GEV) distributions, kth largest maxima, records
- Multivariate extreme value distributions
2016 lecture notes in one file
Literature
Lecture diary
- week 1 (12th Feb): convergence in distribution, central limit theorem and its proof using characteristic functions, properties of characteristic functions, domains of attraction, example for symmetric stable laws
- week 2 (19th Feb): example for symmetric stable laws and their characteristic function, non-symmetric stable laws and their scaling, special stable laws, characterization of stable laws as limits of sums of iid sequences, convergence of types theorem
- week 3 (26th Feb): convergence in probability and with probability one (almost surely), almost sure limit of the maximum process without scaling, extreme value distributions, Poisson approximation, discrete examples, max-stable laws and their characterization
- week 4 (4th Mar): Fisher-Tippett theorem, characterization of extreme value distributions
- week 5 (11th Mar): maximum domains of attraction of extreme value distributions, examples for Frechet and Weibull, hazard rate
- week 6 (18th Mar): examples for the maximum domain of attraction of Gumbel, the normal distribution, generalized extreme value distributions, kth largest records
- week 7 (25th Mar): limit theorem for the kth largest record, Poisson point processes, Poisson description of record values, law of large numbers for the number of records, convergence of the rescaled point process of record times
- week 8 (8th Apr): multivariate max-id (maximum infinitely divisible distributions), multivariate max-stable distributions
- week 9 (15th Apr): midterm test