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Bias Reduction for the Maximum Likelihood Estimator of the Parameters of the Generalized Rayleigh Family of Distributions

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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 Rayleigh distribution family. Using these expressions to bias-correct the estimators is found to be extremely effective in terms of bias reduction, and generally results in a small reduction in relative mean squared error. In general, the analytic bias-corrected estimators are also found to be superior to the alternative of bias-correction via the bootstrap.

Suggested Citation

  • David E. Giles & Xiao Ling, 2011. "Bias Reduction for the Maximum Likelihood Estimator of the Parameters of the Generalized Rayleigh Family of Distributions," Econometrics Working Papers 1111, Department of Economics, University of Victoria.
  • Handle: RePEc:vic:vicewp:1111
    Note: ISSN 1485-6441
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    File URL: http://www.uvic.ca/socialsciences/economics/assets/docs/econometrics/ewp1111.pdf
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    References listed on IDEAS

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    1. Beenstock, Michael, 1995. "The stochastic economics of windpower," Energy Economics, Elsevier, vol. 17(1), pages 27-37, January.
    2. Meagher Kieron J & Teo Ernie G.S. & Wang Wen, 2008. "A Duopoly Location Toolkit: Consumer Densities Which Yield Unique Spatial Duopoly Equilibria," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 8(1), pages 1-23, April.
    3. Clements, Kenneth W & Selvanathan, Antony & Selvanathan, Saroja, 1996. "Applied Demand Analysis: A Survey," The Economic Record, The Economic Society of Australia, vol. 72(216), pages 63-81, March.
    4. Cordeiro, Gauss M. & Klein, Ruben, 1994. "Bias correction in ARMA models," Statistics & Probability Letters, Elsevier, vol. 19(3), pages 169-176, February.
    5. Aigner, Dennis & Lovell, C. A. Knox & Schmidt, Peter, 1977. "Formulation and estimation of stochastic frontier production function models," Journal of Econometrics, Elsevier, vol. 6(1), pages 21-37, July.
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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

    More about this item

    Keywords

    Generalized Rayleigh distribution; maximum likelihood; bias; mean squared error; bias correction;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions

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