Course syllabus

# Statistisk modellering av multivariata extremvärden

Statistical Modelling of Multivariate Extreme Values

## FMSN15, 7,5 credits, A (Second Cycle)

## General Information

## Aim

## Learning outcomes

## Contents

## Examination details

## Admission

Admission requirements:## Reading list

## Contact and other information

Statistical Modelling of Multivariate Extreme Values

Valid for: 2017/18

Decided by: PLED I

Date of Decision: 2017-04-10

Elective for: F5, F5-fm, I5-fir, Pi5

Language of instruction: The course will be given in English on demand

Multivariate extreme values occure in, e.g., economy, safety and reliability, insurance mathematics, hydrology, meteorology. environmental sciences, och ocenanography. They often show complicated dependencies between several variables, e.g. between wind speed, wind direction, wave height and ocean currents. This calls for special methods that can be used, e.g., for analysis of trends, calculation of flooding risks, and modelleling storm damage, corrosion speed, or financial risks. Climat and environmental changes, as well as an increasingly complicated financial market, pose new demands on deapend knowledge in these fields. This course is a countinuation of FMS155 Statistical Modelling of Extreme Values, and teaches methods for analysis of multivariate and spatial extreme values.

Knowledge and understanding

For a passing grade the student must

- describe how to define extreme values for multivariate samples,
- describe different characterisations of multivariate extreme value distributions and the relationship between them,
- explain how to generalize the "peaks over threshold"-model to higher dimensions and which asymptotic distributions arise,
- explain which statistical methods can be used for the analysis of extreme values.

Competences and skills

For a passing grade the student must

- handle multivariate data for analysis of extreme values,
- fit extreme value distribution using different methods,
- validate the valitidy of the extreme value model and make suitable modifications of the model,
- use the resulting model for prediction,
- use a statistical computer program for analysis of data,
- present the analysis and conclusions of a practical problem in a written report.

Judgement and approach

For a passing grade the student must

- always check the prerequisites befor stating an extreme value model,
- evaluate the plausibility of a performed study,
- reflect over the limitations of the chosen model and estimation method, as well as alternative solutions.

Weak convergence for normalized extreme values of stochastic vectors, different characterisations of multivariate extreme value distributions, "peaks over threshold"-model in the multivariate case, different definitions of multivariate generalized Pareto distributions, statistical inference for multivariate extreme values, parametric and semi-parametric methods for multivariate extreme values, use of copula in modelling extreme values, point process characterisation of extreme values, prediction of extreme values, examples of applications of the theory, e.g., estimation of operational risk, climate changes and wind insurances.

Grading scale: TH - (U,3,4,5) - (Fail, Three, Four, Five)

Assessment: Written exam and home assignments.

The examiner, in consultation with Disability Support Services, may deviate from the regular form of examination in order to provide a permanently disabled student with a form of examination equivalent to that of a student without a disability.

Parts

Code: 0116. Name: Written Examination.

Credits: 6. Grading scale: TH. Assessment: Written examination.

Code: 0216. Name: Laboratory Work Part 1.

Credits: 0,5. Grading scale: UG. Assessment: Laboratory work 1 with written assignment.

Code: 0316. Name: Laboratory Work Part 2.

Credits: 1. Grading scale: UG. Assessment: Computer exercise 2 and 3 with written assignments

Code: 0416. Name: Laboratory Work Intro.

Credits: 0. Grading scale: UG. Assessment: Computer exercise Contents: Basic extreme value theory for students with FMS065 Further information: Optional for students who have passed FMS155.

- FMS065 Statistical Methods for Safety Analysis or FMS155 Statistical Modelling of Extreme Values or FMSF60 Statistical Methods for Safety Analysis or FMSN55 Statistical Modelling of Extreme Values

The number of participants is limited to: No

The course overlaps following course/s: MASM23

- Jan Beirlant, Yuri Goegebeur, Johan Segers, Jozef Teugels: Statistics of Extremes: Theory and Applications. Wiley, 2004, ISBN: 978-0471976479.
- Roger B. Nelson: An Introduction to Copulas. Springer, 2006, ISBN: 978-0387286594. E-book.

Course coordinator: Docent Nader Tajvidi, nader@maths.lth.se

Director of studies: Anna Lindgren, studierektor@matstat.lu.se

Course homepage: http://www.maths.lth.se/matstat/kurser/fmsn15/

Further information: The course is also given at the faculty of science with the course code MASM23.