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