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ST803: Extreme Value Statistics (5 ECTS)

STADS: 25001901

Level
Master's level course approved as PhD course

Teaching period
The course is offered in the autumn semester.
The course is offered when needed.

Teacher responsible
Email: yuri.goegebeur@imada.sdu.dk

Timetable
Group Type Day Time Classroom Weeks Comment
Common I Monday 12-14 IMADA semi 6-12,15-16
Common I Wednesday 08-10 U146 6
Common I Wednesday 10-12 U82A 8
Common I Wednesday 08-10 IMADA semi 10
Common I Wednesday 10-12 U60 12
H1 TE Wednesday 10-12 U17 7
H1 TE Wednesday 08-10 IMADA semi 9,11,15
H1 TE Wednesday 12-14 U141 16
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Comment:
Ubegrænset deltagerantal

Prerequisites:
None

Academic preconditions:
Students taking the course are expected to:
  • Have knowledge of mathematical statistics and probability theory
 


Course introduction
The aim of the course is to enable the student to work in a rigorous way with probability models for extreme values, which is important in regard to modelling of extreme events, e.g. in finance and insurance.

The course builds on the knowledge acquired in the courses ST521 Mathematical Statistics and MM544 Probability Theory, and gives an academic basis for master thesis projects in extreme values.

In relation to the competence profile of the degree it is the explicit focus of the course to:
  • 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
The learning objectives of the course is that the student demonstrates the ability to:
  • 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
 


Subject overview
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
    Meddeles ved kursets start


Website
This course uses e-learn (blackboard).

Prerequisites for participating in the exam
None

Assessment and marking:
  1. Oral exam, internal marking, 7-mark scale. The oral exam is based on but not limited to a project assignment. No exam aids allowed, a closer description of the exam rules will be posted under 'Course Information' on Blackboard. (5 ECTS). (25001902).
The re-exam can be of another form than the original exam.

Expected working hours
The teaching method is based on three phase model.
Intro phase: 28 hours
Skills training phase: 12 hours, hereof:
 - Tutorials: 12 hours

Educational activities
  • Studying the course material and preparing the weekly exercises, individually or through group work
Educational form
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.

Language
This course is taught in Danish or English, depending on the lecturer. However, if international students participate, the teaching language will always be English.

Course enrollment
See deadline of enrolment.

Tuition fees for single courses
See fees for single courses.