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Bias - Corrected Maximum Likelihood Estimation of the Parameters of the Generalized Pareto Distribution


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We 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 Info

Paper provided by Department of Economics, University of Victoria in its series Econometrics Working Papers with number 1105.

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Length: 26 pages
Date of creation: 11 Oct 2011
Date of revision:
Handle: RePEc:vic:vicewp:1105

Note: ISSN 1485-6441
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Postal: PO Box 1700, STN CSC, Victoria, BC, Canada, V8W 2Y2
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Keywords: Bias reduction; Extreme values; Generalized Pareto distribution; Peaks over threshold; Parametric bootstrap;

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Blog mentions

As found by, the blog aggregator for Economics research:
  1. Extremes, the Generalized Pareto Distribution, and MLE
    by Dave Giles in Econometrics Beat: Dave Giles' Blog on 2012-04-19 22:03:00
  2. Bias-Corrected MLEs
    by Dave Giles in Econometrics Beat: Dave Giles' Blog on 2012-05-01 16:03:00
  3. What I Learned Last Week
    by Dave Giles in Econometrics Beat: Dave Giles' Blog on 2012-10-13 04:19:00
  4. N.Z. Econometrics Study Group
    by Dave Giles in Econometrics Beat: Dave Giles' Blog on 2013-02-06 03:09:00
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Cited by:
  1. 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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