Extreme Value Theory with Implementation in S-PLUS


Extreme value theory has been subject of much practical and theoretical work in the last few years. Recent developments have introduced very flexible and theoretically well motivated semi-parametric models for extreme values which now are at the stage where they can be used to address important technological problems on handling risks in areas such as wind engineering, hydrology, flood monitoring and prediction, climatic changes, structural reliability, corrosion modelling, and large insurance claims or large fluctuations in financial data (volatility).

This course is mainly for mathematical statistics graduate students and will give an overview of a number of different topics in modern extreme value thoery (of course interested faculty are always welcome). These topics will include the following:

The objective of the course is two-folded. Firstly, we intend to cover the probability theory of univariate and multivariate extreme value theory in the case of independent variables. Our approach will be mainly from applied point of view so statistical modeling of extreme events will be main emphasis of the course. As a modeling language we will be using S-PLUS so the secondary goal of the course is that, upon completing the course, participants will be able to use and write programs in S-PLUS for their own applications. To this end we will discuss a few examples of applications of the extreme value theory in S-PLUS in details. These example are mainly taken from a few papers which have recently been published and we will go through the details of calculations which are behind the results presented in the papers. We will als cover the fundamentals of S-PLUS which are necessary for statistical modeling in general. This will include: The course will meet two times a week (2x45 each time) for the first reading period and perhaps part of the second reading period. At the time, the preliminary plan of the course is that each part of the course will take up about half of the lectures. Each lecture will concentrate only either in extreme value theory or S-PLUS programming so participants who wish to follow only one part of the course will be able to attend only those lectures which are of interest to them. The course will give 8 graduate points (5p for extreme values and 3p for S-PLUS).

Literature

During the course we will use material presented in various papers. I will try to hand out in advance copies of the papers to those participants who follow extreme value part of the course. The following books will be the main references:

  1. Leadbetter, M.R., Lindgren, G. and Rootz\'en, H. (1983) Extremes and Related Properties of Random Sequences and Processes, Berlin: Springer-Verlag.
  2. Resnick, S.I. (1987) Extreme values, Regular Variation and Point Processes, Berlin: Springer-Verlag.
  3. Embrechts P. , Kluppelberg C., Mikosch T. (1997) Modelling Extremal Events , Berlin: Springer-Verlag.
  4. 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.
  5. Becker, R.A., Chambers J.M. and Wilks A.R. (1988) The new S Language, A Programming Environment For Data Analysis and Graphics, Wadsworth and Brooks/Cole Computer Science Series.
  6. Chambers J. M., Hastie, T. (1992) Statistical Models in S Wadsworth and brooks/cole Computer Science Series.
  7. Chambers J. M. (1998) Programming with data: A guide to the S language New York: Springer-Verlag. See the homepage of the book here .
  8. Venables W.N. , Ripley B.D. (1999) Modern Applied Statistics with S-PLUS Vol 1: Data Analysis Springer-Verlag. See the homepage of the book here.
  9. Venables W.N. , Ripley B.D. (2000) S Programming Springer-Verlag. See the homepage of the book here.

Last modified: Wed Oct 3 16:47:59 MEST 2001