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Bias of the Maximum Likelihood Estimators of the Two-Parameter Gamma Distribution Revisited

We consider the quality of the maximum likelihood estimators for the parameters of the two-parameter gamma distribution in small samples. We show that the methodology suggested by Cox and Snell (1968) can be used very easily to bias-adjust these estimators. A simulation study shows that this analytic correction is frequently much more effective than bias-adjusting using the bootstrap – generally by an order of magnitude in percentage terms. The two bias-correction methods considered result in increased variability in small samples, and the original estimators and their bias-corrected counterparts all have similar percentage mean squared errors.

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File URL: http://www.uvic.ca/socialsciences/economics/assets/docs/econometrics/ewp0908.pdf
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Paper provided by Department of Economics, University of Victoria in its series Econometrics Working Papers with number 0908.

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Length: 19 pages
Date of creation: 23 Sep 2009
Date of revision:
Handle: RePEc:vic:vicewp:0908
Note: ISSN 1485-6441
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Web page: http://web.uvic.ca/econ

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  1. 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.
  2. 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.
  3. Cordeiro, Gauss M. & Klein, Ruben, 1994. "Bias correction in ARMA models," Statistics & Probability Letters, Elsevier, vol. 19(3), pages 169-176, February.
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