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Analytic Bias Correction for Maximum Likelihood Estimators When the Bias Function is Non-Constant

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Abstract

Recently, many papers have obtained analytic expressions for the biases of various maximum likelihood estimators, despite their lack of closed-form solution. These bias expressions have provided an attractive alternative to the bootstrap. Unless the bias function is “flat,” however, the expressions are being evaluated at the wrong point(s). We propose an “improved” analytic bias adjusted estimator, in which the bias expression is evaluated at a more appropriate point (at the bias adjusted estimator itself). Simulations illustrate that the improved analytic bias adjusted estimator can eliminate significantly more bias than the simple estimator which has been well established in the literature.

Suggested Citation

  • 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.
    • Handle: RePEc:vic:vicewp:1702
    Note: ISSN 1485-6441
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    References listed on IDEAS

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    1. Ryan T. Godwin, 2016. "Bias reduction for the maximum likelihood estimator of the doubly-truncated Poisson distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(7), pages 1887-1901, April.
    2. Jacob Schwartz & David E. Giles, 2016. "Bias-reduced maximum likelihood estimation of the zero-inflated Poisson distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(2), pages 465-478, January.
    3. Jacob Schwartz & Ryan T. Godwin & David E. Giles, 2011. "Improved Maximum Likelihood Estimation of the Shape Parameter in the Nakagami Distribution," Econometrics Working Papers 1109, Department of Economics, University of Victoria.
    4. MacKinnon, James G. & Smith Jr., Anthony A., 1998. "Approximate bias correction in econometrics," Journal of Econometrics, Elsevier, vol. 85(2), pages 205-230, August.
    5. 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.
    6. David E. Giles & Hui Feng & Ryan T. Godwin, 2016. "Bias-corrected maximum likelihood estimation of the parameters of the generalized Pareto distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(8), pages 2465-2483, April.
    7. Cordeiro, Gauss M. & Vasconcellos, Klaus L. P., 1997. "Bias correction for a class of multivariate nonlinear regression models," Statistics & Probability Letters, Elsevier, vol. 35(2), pages 155-164, September.
    8. Cordeiro, Gauss M. & Klein, Ruben, 1994. "Bias correction in ARMA models," Statistics & Probability Letters, Elsevier, vol. 19(3), pages 169-176, February.
    9. Arne Henningsen & Ott Toomet, 2011. "maxLik: A package for maximum likelihood estimation in R," Computational Statistics, Springer, vol. 26(3), pages 443-458, September.
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    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

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