Abstract #301021

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JSM 2002 Abstract #301021
Activity Number: 146
Type: Contributed
Date/Time: Monday, August 12, 2002 : 2:00 PM to 3:50 PM
Sponsor: Section on Risk Analysis*
Abstract - #301021
Title: Estimating the Probability of a Rare Event
Author(s): Ashoke Sinha*+ and Laurens de Haan
Affiliation(s): Tilburg University and Erasmus University Rotterdam
Address: Warandelaan 2, Postbus 90153, Tilburg, , 5000 LE, The Netherlands
Keywords: rare event ; extreme value theory
Abstract:

Let (X,Y), (X1,Y1), (X2,Y2),...., (Xn,Yn) be a random sample from a bivariate distribution function F, which is in the domain of attraction of a bivariate extreme value distribution function G. Suppose C is a subset of R^2, which contains none of the observations. We want to estimate the probability p that (X,Y) falls in C. Since none of the observations falls in C, empirical distributions does not provide any useful estimate. In this presentation, we shall suggest a non-parametric estimator for p and construct an asymptotic confidence interval for p under certain conditions.

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Revised March 2002