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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 generally results in some reduction in relative mean squared error. The analytic bias-corrected estimators are also shown to be dramatically superior to the alternative of bias-correction via the bootstrap.

Suggested Citation

  • 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.
  • Handle: RePEc:vic:vicewp:0902 Note: ISSN 1485-6441
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    References listed on IDEAS

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    1. Giles, David E. A. & Srivastava, Virendra K., 1993. "The exact distribution of a least squares regression coefficient estimator after a preliminary t-test," Statistics & Probability Letters, Elsevier, vol. 16(1), pages 59-64, January.
    2. Giles, Judith A & Giles, David E A, 1993. " Pre-test Estimation and Testing in Econometrics: Recent Developments," Journal of Economic Surveys, Wiley Blackwell, vol. 7(2), pages 145-197, June.
    3. Giles, Judith A., 1991. "Pre-testing for linear restrictions in a regression model with spherically symmetric disturbances," Journal of Econometrics, Elsevier, vol. 50(3), pages 377-398, December.
    4. Giles, David E. A., 1993. "Pre-test estimation in regression under absolute error loss," Economics Letters, Elsevier, vol. 41(4), pages 339-343.
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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;

    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
    • C41 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Duration Analysis; Optimal Timing Strategies
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions

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