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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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    File URL: https://www.uvic.ca/socialsciences/economics/_assets/docs/econometrics/ewp0902.pdf
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    Blog mentions

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

    Citations

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    Cited by:

    1. David E. Giles, 2021. "Improved Maximum Likelihood Estimation for the Weibull Distribution Under Length-Biased Sampling," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(1), pages 59-77, December.
    2. Joseph Reath & Jianping Dong & Min Wang, 2018. "Improved parameter estimation of the log-logistic distribution with applications," Computational Statistics, Springer, vol. 33(1), pages 339-356, March.
    3. El-Sherpieny, El-Sayed A. & Almetwally, Ehab M. & Muhammed, Hiba Z., 2020. "Progressive Type-II hybrid censored schemes based on maximum product spacing with application to Power Lomax distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 553(C).
    4. Ryan T. Godwin & David E. Giles, 2017. "Analytic Bias Correction for Maximum Likelihood Estimators When the Bias Function is Non-Constant," Econometrics Working Papers 1702, Department of Economics, University of Victoria.
    5. Marc N. Conte & David L. Kelly, 2016. "An Imperfect Storm: Fat-Tailed Hurricane Damages, Insurance and Climate Policy," Working Papers 2016-01, University of Miami, Department of Economics.
    6. Conte, Marc N. & Kelly, David L., 2018. "An imperfect storm: Fat-tailed tropical cyclone damages, insurance, and climate policy," Journal of Environmental Economics and Management, Elsevier, vol. 92(C), pages 677-706.
    7. David E. Giles, 2012. "A Note on Improved Estimation for the Topp-Leone Distribution," Econometrics Working Papers 1203, Department of Economics, University of Victoria.
    8. Wolfgang Kössler & Janine Ott, 2019. "Two-sided variable inspection plans for arbitrary continuous populations with unknown distribution," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(3), pages 437-452, September.
    9. 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.
    10. Hideki Nagatsuka & N. Balakrishnan, 2021. "Efficient likelihood-based inference for the generalized Pareto distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(6), pages 1153-1185, December.
    11. Mahdi Teimouri, 2022. "bccp: an R package for life-testing and survival analysis," Computational Statistics, Springer, vol. 37(1), pages 469-489, March.

    More about this item

    Keywords

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    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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