Course Syllabus for

Statistical Modelling of Multivariate Extreme Values
Statistisk modellering av multivariata extremvärden

FMSN15F, 7.5 credits

Valid from: Autumn 2020
Decided by: Professor Thomas Johansson
Date of establishment: 2020-05-19

General Information

Division: Mathematical Statistics
Course type: Course given jointly for second and third cycle
The course is also given at second-cycle level with course code: FMSN15
Teaching language: English

Aim

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 FMSN55 Statistical Modelling of Extreme Values, and teaches methods for analysis of multivariate and spatial extreme values.

Goals

Knowledge and Understanding

For a passing grade the doctoral student must

Competences and Skills

For a passing grade the doctoral student must

Judgement and Approach

For a passing grade the doctoral student must

Course Contents

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.

Course Literature

Instruction Details

Types of instruction: Lectures, laboratory exercises, exercises

Examination Details

Examination formats: Written exam, written assignments
Grading scale: Failed, pass
Examiner:

Admission Details

Admission requirements: FMSN55 Statistical Modelling of Extreme Values

Course Occasion Information

Contact and Other Information

Course coordinators:
Web page: www.maths.lth.se/matstat/kurser/fmsn15/


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