ST803: Extreme Value Statistics

Study Board of Science

Teaching language: Danish or English depending on the teacher, but English if international students are enrolled
EKA: N370002102
Assessment: Second examiner: Internal
Grading: 7-point grading scale
Offered in: Odense
Offered in: Spring
Level: Master's level course approved as PhD course

STADS ID (UVA): N370002101
ECTS value: 5

Date of Approval: 04-11-2021


Duration: 1 semester

Version: Approved - active

Entry requirements

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

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

See itslearning for syllabus lists and additional literature references.

Examination regulations

Exam element a)

Timing

June

Tests

Oral exam

EKA

N370002102

Assessment

Second examiner: Internal

Grading

7-point grading scale

Identification

Student Identification Card

Language

Normally, the same as teaching language

Examination aids

To be announced during the course

ECTS value

5

Indicative number of lessons

40 hours per semester

Teaching Method

The teaching activities are reflected in an estimated allocation of the workload of an average student as follows:
  • Intro phase (lectures) - 28 hours
  • Training phase: 12 hours
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 E-mail Department
Yuri Goegebeur Yuri.Goegebeur@imada.sdu.dk Data Science

Timetable

Administrative Unit

Institut for Matematik og Datalogi (matematik)

Team at Educational Law & Registration

NAT

Offered in

Odense

Recommended course of study

Profile Education Semester Offer period

Transition rules

Transitional arrangements describe how a course replaces another course when changes are made to the course of study. 
If a transitional arrangement has been made for a course, it will be stated in the list. 
See transitional arrangements for all courses at the Faculty of Science.