Modelling Extremal Events

The course is not on the list Without time-table

Code	Completion	Credits	Range	Language
01MEU	ZK	3	2P	Czech

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

1.Aggregated traffic in computer nets, possible admission control, machine learning, on-off approximation.

2.Distribution-free inequalities for tail probability estimation, PC simulation of traffic.

3.Nonparametric density estimators and their tails, asymptotic properties, MISE optimality.

4.Semiparametric estimation, retransformed densities, statistical properties, score functions.

5.Phi-divergences, properties, Kolmogorov entropy, Vapnik-Chervonenkis dimension, application.

6.Fluctuation of random sums, stable and α-stable distributions, their characteristics.

7.Generalized central limit theorem, domains of attraction, sub-exponential distributions.

8.Heavy-tail distribution detections, PP and QQ plots, Mean Excess function, its empirical estimator, usage.

9.Return period of (insurance) events, record counting process, Gumbel method of exceedance.

10.Fluctuation of random maxima, Fisher-Tippett law, max-stability, maximum domain of attraction.

11.Generalized extreme value distribution, generalized Pareto distribution, properties and utilization.

12.Estimates of exceedance over threshold, POT methods, estimator of quantile, application.

13.Applications to real data from hydrology, geology, insurance, finance, numerous other examples.

Requirements:

Syllabus of lectures:

Syllabus of tutorials:

Study Objective:

Study materials:

Key references:

[1] R.-D. Reiss, M. Thomas: Statistical Analysis of Extreme Values: from Insurance, Finance, Hydrology and Other Fields, Birkhäuser Basel, 2014.

[2] S. Foss, D. Korshunov, S. Zachary: An Introduction to Heavy-Tailed and Subexponential Distributions, Springer-Verlag, New York, 2013.

Recommended references:

[3] N. Markovich: Nonparametric Analysis of Univariate Heavy-Tailed Data, Wiley, 2007.

[4] P. Embrechts, C. Klüppelberg, T. Mikosch: Modelling Extremal Events, Springer, New York, 1997.

[5] S. Coles: An Introduction to Statistical Modeling of Extreme Values, Springer, London, 2001.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: