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Bias Reduction for the Maximum Likelihood Estimator of the Scale Parameter in the Half-Logistic Distribution

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Abstract

We derive an analytic expression for the bias, to O(n-1) of the maximum likelihood estimator of the scale parameter in the half-logistic distribution. Using this expression to bias-correct the estimator is shown to be very effective in terms of bias reduction, without adverse consequences for the estimator’s precision. The analytic bias-corrected estimator is also shown to be dramatically superior to the alternative of bootstrap-bias-correction.

Suggested Citation

  • David E. Giles, 2009. "Bias Reduction for the Maximum Likelihood Estimator of the Scale Parameter in the Half-Logistic Distribution," Econometrics Working Papers 0901, Department of Economics, University of Victoria.
    • Handle: RePEc:vic:vicewp:0901
    Note: ISSN 1485-6441
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    File URL: https://www.uvic.ca/socialsciences/economics/_assets/docs/econometrics/ewp0901.pdf
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    References listed on IDEAS

    as
    1. Balakrishnan, N. & Chan, P. S., 1992. "Estimation for the scaled half logistic distribution under Type II censoring," Computational Statistics & Data Analysis, Elsevier, vol. 13(2), pages 123-141, March.
    2. Cordeiro, Gauss M. & Klein, Ruben, 1994. "Bias correction in ARMA models," Statistics & Probability Letters, Elsevier, vol. 19(3), pages 169-176, February.
    3. Adatia, A., 1997. "Approximate BLUEs of the parameters of the half logistic distribution based on fairly large doubly censored samples," Computational Statistics & Data Analysis, Elsevier, vol. 24(2), pages 179-191, April.
    4. Adatia, A., 2000. "Estimation of parameters of the half-logistic distribution using generalized ranked set sampling," Computational Statistics & Data Analysis, Elsevier, vol. 33(1), pages 1-13, March.
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    Blog mentions

    As found by EconAcademics.org, the blog aggregator for Economics research:
    1. Bias-Corrected MLEs
      by Dave Giles in Econometrics Beat: Dave Giles' Blog on 2012-05-01 21:03:00

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    Cited by:

    1. Jacob Schwartz & David E. Giles, 2011. "Biased-Reduced Maximum Likelihood Estimation for the Zero-Inflated Poisson Distribution," Econometrics Working Papers 1102, Department of Economics, University of Victoria.
    2. 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.
    3. David E Giles & Hui Feng, 2011. "Reducing the bias of the maximum likelihood estimator for the Poisson regression model," Economics Bulletin, AccessEcon, vol. 31(4), pages 2933-2943.

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    More about this item

    Keywords

    Half-logistic distribution; Life testing; Bias reduction;
    All these keywords.

    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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