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

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Abstract

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.

Suggested Citation

  • David E. Giles & Hui Feng & Ryan T. Godwin, 2011. "Bias - Corrected Maximum Likelihood Estimation of the Parameters of the Generalized Pareto Distribution," Econometrics Working Papers 1105, Department of Economics, University of Victoria.
  • Handle: RePEc:vic:vicewp:1105
    Note: ISSN 1485-6441
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    File URL: http://www.uvic.ca/socialsciences/economics/assets/docs/econometrics/ewp1105.pdf
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    Blog mentions

    As found by EconAcademics.org, the blog aggregator for Economics research:
    1. Extremes, the Generalized Pareto Distribution, and MLE
      by Dave Giles in Econometrics Beat: Dave Giles' Blog on 2012-04-20 03:03:00
    2. Bias-Corrected MLEs
      by Dave Giles in Econometrics Beat: Dave Giles' Blog on 2012-05-01 21:03:00
    3. What I Learned Last Week
      by Dave Giles in Econometrics Beat: Dave Giles' Blog on 2012-10-13 09:19:00
    4. N.Z. Econometrics Study Group
      by Dave Giles in Econometrics Beat: Dave Giles' Blog on 2013-02-06 09:09:00

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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.

    More about this item

    Keywords

    Bias reduction; Extreme values; Generalized Pareto distribution; Peaks over threshold; Parametric bootstrap;

    JEL classification:

    • 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

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