School Seminars and Colloquia

Multilevel clustering of extremes

Complex Systems Seminar

by Dr S.Yu.Novak


Institution: Middlesex University, UK
Date: Fri 13th July 2007
Time: 3:15 PM
Location: Room 213, Richard Berry Building, Department of Mathematics and Statistics, The University of Melbourne

Abstract: A sample element, Xi, is considered “extreme’’ if it exceeds a certain level un. Various
quantities of interest in Extreme Value Theory can be expressed in terms of the number
of exceedances, Nn(u) = S1
n 1{Xi > u}. For example, the distribution of the sample
maximum, Mn, is closely related to that of Nn: {Mn>u} = {Nn(u)>0}.
The process {Nn(u), u³un} describes exceedances of several levels. The topic is of
interest to insurers as an insurance company may be interested in a number of claims
varying between certain levels. The empirical point process of exceedances (EPPE)
{N[sn](u), u³un, s³0} takes into account heights as well as locations of extremes.
EPPE’s play a central role in Extreme Value theory. We describe the class of limit laws
for EPPE’s, and present necessary & sufficient conditions for the weak convergence of an
EPPE to a given element of that class.

For More Information: Gerard Healy +61 3 8344 1795 g.healy@ms.unimelb.edu.au