Teaching plan for extreme value theory

1. Coles S. (2001) An Introduction to Statistical Modelling of Extreme Values Springer-Verlag London. You can order the book e.g. at amazon. See also the homepage of the book here.
2. Leadbetter, M.R., Lindgren, G. and Rootz\'en, H. (1983) Extremes and Related Properties of Random Sequences and Processes, Berlin: Springer-Verlag.
3. Resnick, S.I. (1987) Extreme values, Regular Variation and Point Processes, Berlin: Springer-Verlag.
4. Embrechts P. , Kluppelberg C., Mikosch T. (1997) Modelling Extremal Events, Berlin: Springer-Verlag.

Lecture 1

Contents:
Limit probabilities for maxima. Weak convergence of maxima under affine transformations. Extremal types theorem. The generalised extreme value (GEV) distribution. Asymptotic models for minima.

Lecture 2

Contents:
Inference for the GEV. Maximum likelihood estimation. Small sample properties of ML-estimators. Calculation of standard errors. Profile likelihood.

Lecture 3

Contents:
Peaks over threshold model. The generalised Pareto distribution (GPD). Inference for GPD. Threshold selection.

Lecture 4

Contents:
Parametric and non-parametric analysis of temporal trend in extreme values with applications to wind storm losses and temperature data.

Lecture 5

Contents:
Multivariate extremes. Characterizing Max-Stable distributions. Point process representation.

Lecture 6

Contents:
Generalisation of peaks over threshold model to multivariate case.

Lecture 7

Contents:
Inference for multivariate extremes. Parametric and non parametric methods for estimation of dependence function in bivariate extremes. Prediction of extremes.