ST803: Extreme Value Statistics
Comment
Entry requirements
Academic preconditions
- Have knowledge of mathematical statistics and probability theory
Course introduction
rigorous way with probability models for extreme values, which is
important in regard to modelling of extreme events, e.g. in finance and
insurance.
in the courses ST521 Mathematical Statistics and MM544 Probability
Theory, and gives an academic basis for master thesis projects in
extreme values.
- Give the competence to handle model building and model calculations
- Give skills to perform statistical analysis
- Give theoretical knowledge and practical experience with the application of methods and models from statistics
Expected learning outcome
- reproduce the theoretical results concerning the convergence of maxima and excesses over a threshold
- verify if a distribution is in the domain of attraction of the generalized extreme value distribution
- verify if a distribution function satisfies the second order condition on tail behavior
- describe
the principles of tail index estimation and extreme quantile
estimation, and to apply these in a given practical setting - perform programming relevant to the content of the course in the statistical package used in the course
- identify and interpret relevant information in the output of the statistical package used in the course
- summarize the results of an extreme value analysis in a statistical report
Content
The following main topics are contained in the course:
Graphical tools for tail analysis, order statistics, convergence of normalized sample maxima, domain of attraction of the generalized extreme value distribution, convergence of excesses over thresholds, the generalized Pareto distribution, second order tail behavior, estimation of the tail index, extremes in regression analysis.
Literature
Examination regulations
Exam element a)
Timing
Tests
Oral exam
EKA
Assessment
Grading
Identification
Language
Examination aids
No exam aids allowed, a closer description of the exam rules will be posted under 'Course Information' on Blackboard.
ECTS value
Additional information
The examination form for re-examination may be different from the exam form at the regular exam.
Indicative number of lessons
Teaching Method
In the intro phase a modified version of the classical
lecture is employed, where the terms and concepts of the topic are
presented, from theory as well as from examples based on actual data. In
these hours there is room for questions and discussions.
In the training phase
the students work with data-based problems and discussion topics,
related to the content of the previous lectures in the intro phase. In
these hours there is a possibility of working specifically with selected
difficult concepts.
In the study phase the
students work independently with problems and the understanding of the
terms and concepts of the topic. Questions from the study phase can
afterwards be presented in either the intro phase hours or the training
phase hours.
Educational activities
- Studying the course material and preparing the weekly exercises, individually or through group work
Teacher responsible
Name | Department | |
---|---|---|
Yuri Goegebeur | Yuri.Goegebeur@imada.sdu.dk | Institut for Matematik og Datalogi |