May 17, 2005

EURANDOM, Laplace Building TU/e, Green Lecture Room (LG 1.105)





Welcome and introduction

Professor Kees van Hee, Dean Department of Mathematics and Computer Science TU/e

Professor Onno Boxma, Scientific Advisor EURANDOM programme QPA and Chairman of the Mathematics Division of the Department of Mathematics and Computer Science TU/e

Professor Sid Resnick, School of Operations Research and Industrial Engineering, Cornell University
Multivariate heavy tails, asymptotic independence and beyond
A random vector having a distribution which is multivariate regularly varying at infinity can have a dependence structure which is hard to specify in practice. One extreme but not uncommon case  is ''asymptotic independence'' which roughly describes the situation where the random vector's components are not simultaneously large. In the absence of fruther assumptions, estimation of the probability of extreme risk sets yields estimates which are null. One way to remedy this is through hidden regular variation which measures variables on a different scale. Another is via conditioning on one component being large and using a limiting distribution as the conditioning variable is pushed to infinity We discuss detection of hidden regular variation along with other extensions into conditional models. An application to network data is provided.

Biography of Sid Resnick

Resnick joined the Cornell faculty in 1987 after nine years at Colorado State University, six years at Stanford University, and two years at the Technion, in Haifa, Israel. He has also held visiting appointments at several institutions, including the University of Amsterdam and the Amsterdam Mathematics Center; the Australian National University and CSIRO, in Canberra, Australia; the Technion in Israel (as a Lady Davis Fellow); Sussex University, in Brighton, UK (as a Science and Engineering Research Council Fellow), Erasmus University, in Rotterdam, The Netherlands; and ETH Zurich. Resnick is a fellow of the Institute of Mathematical Statistics, and while at Colorado State was an Oliver Pennock Distinguished Service Award winner. He was on the Bernoulli Society Committee for Conferences in Stochastic Processes and was on the program committee of the First World Congress of the Bernoulli Society in Tashkent, USSR.

He is a founding associate editor of Annals of Applied Probability, and a current associate editor of Journal of Applied Probability, Stochastic Models, and The Mathematical Scientist. He is a former associate editor of Stochastic Processes and Their Applications. He served a three-year term on the Council of the Institute of Mathematical Statistics and served on their ad hoc committee on electronic publishing. He is currently an editor for Birkhauser, Boston serving on the boards of the Progress in Probability and Progress in Probability and Its Applications series. He is the author of four books and numerous papers. During the past five years he has served as Director of Cornell's School of Operations Research and Industrial Engineering.


17.00 h... Reception


The MINI-COURSE on "Heavy tailed analysis" is scheduled on

May 24, May 3, June 7 & June 14, 2005, 13.30-15.15 h., EURANDOM Lecture room LG 1.105

The series will survey the mathematical, probabilistic and statistical tools used in heavy tail analysis. Heavy tails are characteristic of phenomena where the probability of an huge value is relatively big. Record breaking insurance losses, financial log-returns, file sizes stored on a server, transmission rates of files are all examples of heavy tailed phenomena. The modeling and statistics of such phenomena are tail dependent and much different than classical modeling and statistical analysis which give primacy to central moments, averages and the normal density, which has a wimpy, light tail. An organizing theme is that many limit relations giving approximations can be viewed as mere applications of continuous maps


May 24th, 2005
1. Introduction
2. Survey of the theory of regular variation.
3. Survey of weak convergence (spaces: R, sequences, C, D, measures and point measures; vague convergence; relation with regular variation).
Lecture notes

May 31, 2005
1. Tail empirical measure Hill
2. Pickands estimators of tail indices.
Lecture notes

June 7, 2005

1. Asymptotic normality of the tail empirical measure; application to Hill estimator.
2. Applications of the Poisson process; the infinite source Poisson model.
Lecture notes

June 14, 2005
1. Laplace functional
2. Poisson transform; point process method
3. Transformations for heavy tails
4. Sample of topics not covered
Lecture notes

The complete course will be published as EURANDOM report.