Bias - Corrected Maximum Likelihood Estimation of the Parameters of the Generalized Pareto Distribution
AbstractWe derive analytic expressions for the biases, to O(n-1), of the maximum likelihood estimators of the parameters of the generalized Pareto distribution. Using these expressions to bias-correct the estimators is found to be extremely effective in terms of bias reduction, and can also result in a small reduction in relative mean squared error. In terms of remaining relative bias, the analytic bias-corrected estimators are somewhat less effective than their counterparts obtained by using a parametric bootstrap bias correction. However, the analytic correction out-performs the bootstrap correction in terms of remaining %MSE. Taking into account the relative computational costs, this leads us to recommend the use of the analytic bias adjustment for most practical situations.
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Bibliographic InfoPaper provided by Department of Economics, University of Victoria in its series Econometrics Working Papers with number 1105.
Length: 26 pages
Date of creation: 11 Oct 2011
Date of revision:
Note: ISSN 1485-6441
Contact details of provider:
Postal: PO Box 1700, STN CSC, Victoria, BC, Canada, V8W 2Y2
Web page: http://web.uvic.ca/econ
More information through EDIRC
Bias reduction; Extreme values; Generalized Pareto distribution; Peaks over threshold; Parametric bootstrap;
Other versions of this item:
- David E. Giles & Hui Feng, 2009. "Bias - Corrected Maximum Likelihood Estimation of the Parameters of the Generalized Pareto Distribution," Econometrics Working Papers 0902, Department of Economics, University of Victoria.
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
- C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
- C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
- C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-04-30 (All new papers)
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Blog mentionsAs found by EconAcademics.org, the blog aggregator for Economics research:
- Extremes, the Generalized Pareto Distribution, and MLE
by Dave Giles in Econometrics Beat: Dave Giles' Blog on 2012-04-19 22:03:00
- Bias-Corrected MLEs
by Dave Giles in Econometrics Beat: Dave Giles' Blog on 2012-05-01 16:03:00
- What I Learned Last Week
by Dave Giles in Econometrics Beat: Dave Giles' Blog on 2012-10-13 04:19:00
- N.Z. Econometrics Study Group
by Dave Giles in Econometrics Beat: Dave Giles' Blog on 2013-02-06 03:09:00
- David E. Giles & Hui Feng, 2009. "Bias of the Maximum Likelihood Estimators of the Two-Parameter Gamma Distribution Revisited," Econometrics Working Papers 0908, Department of Economics, University of Victoria.
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