JSM 2005 - Toronto

Abstract #303499

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Legend: = Applied Session, = Theme Session, = Presenter
Activity Number: 103
Type: Contributed
Date/Time: Monday, August 8, 2005 : 8:30 AM to 10:20 AM
Sponsor: IMS
Abstract - #303499
Title: Confidence Intervals for Extreme-tail Probabilities of a Heavy-tailed Distribution
Author(s): Yongcheng Qi*+ and Xiaoyue Niu
Companies: University of Minnesota and University of Minnesota
Address: Dept of Mathematics and Statistics UMD, Duluth, MN, 55812, United States
Keywords: Confidence interval ; Heavy-tailed distribution ; Tail probability ; Empirical likelihood ; Data tilting
Abstract:

In extreme-value statistics, prediction of the occurrence of rare events involves estimating the extreme-tail probabilities of an unknown distribution function beyond the range of the data. In this presentation, we are interested in constructing the confidence intervals for the extreme-tail probabilities of a heavy-tailed distribution. We investigate two methods, including the normal approximation method based on a point estimator and the data tilting method. We show both methods yield asymptotically accurate confidence intervals. Through simulation studies, we compare the coverage probabilities and lengths of the confidence intervals for the two methods.

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