Statistical Modelling of Multivariate Extreme Values
Statistisk modellering av multivariata extremvärden

FMSN15F, 7.5 högskolepoäng

Gäller från och med: Autumn 2020
Beslutad av: Professor Thomas Johansson
Datum för fastställande: 2020-05-19

Allmänna uppgifter

Avdelning: Mathematical Statistics
Kurstyp: Gemensam kurs, avancerad nivå och forskarnivå
Kursen ges även på avancerad nivå med kurskod: FMSN15
Undervisningsspråk: English

Syfte

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.

Mål

Kunskap och förståelse

För godkänd kurs skall doktoranden

• 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.

Färdighet och förmåga

För godkänd kurs skall doktoranden

• 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.

Värderingsförmåga och förhållningssätt

För godkänd kurs skall doktoranden

• 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.

Kursinnehåll

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.

Kurslitteratur

• Beirlant, J., Goegebeur, Y., Segers, J. & Teugels, J.: Statistics of Extremes: Theory and Applications. Wiley, 2004.
• Nelson, Roger B.: An Introduction to Copulas. Springer, 2006.

Kursens undervisningsformer

Undervisningsformer: Föreläsningar, laborationer, övningar

Kursens examination

Examinationsformer: Skriftlig tentamen, inlämningsuppgifter
Betygsskala: Underkänd, godkänd
Examinator:

Antagningsuppgifter

Förkunskapskrav: FMSN55 Statistical Modelling of Extreme Values

Kurstillfällesinformation

Kontaktinformation och övrigt

Kursansvarig: Nader Tajvidi <nader.tajvidi@matstat.lu.se>
Hemsida: www.maths.lth.se/matstat/kurser/fmsn15/