This is the program for the 2010 Joint Statistical Meetings in Vancouver, British Columbia.

Abstract Details

Activity Number: 517
Type: Contributed
Date/Time: Wednesday, August 4, 2010 : 10:30 AM to 12:20 PM
Sponsor: Business and Economic Statistics Section
Abstract - #306497
Title: Almost Unbiased Maximum Likelihood Estimation for the Generalized Pareto Distribtion and Value at Risk
Author(s): David E. Giles*+ and Hui Feng
Companies: University of Victoria and King's College/The University of Western Ontario
Address: P.O. Box 1700, STN CSC, Victoria, BC, V8W 2Y2, Canada
Keywords: Extreme values ; Generalized Pareto distribution ; Value at Risk ; Maximum likelihood estimation ; Bias reduction

The generalised Pareto distribution is widely used to model extreme events, such as in financial markets. We derive analytic expressions for the biases, to O(n^-1) of the maximum likelihood estimators of the parameters of the generalized Pareto distribution and of the implied estimator of the associated Value at Risk. Using these expressions to bias-correct these estimators is found to be extremely effective in terms of bias reduction, and also often results in a small reduction in relative mean squared error. In general, the analytic bias-corrected estimators are also found to be superior to the alternative of bias-correction via the bootstrap. Our results provide modified estimators that can be used by practitioners who model extreme events from relatively small samples of exceedances, using the peaks-over-theshold method.

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