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Median bias reduction of maximum likelihood estimates

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  • E C Kenne Pagui
  • A Salvan
  • N Sartori

Abstract

For regular parametric problems, we show how median centring of the maximum likelihood estimate can be achieved by a simple modification of the score equation. For a scalar parameter of interest, the estimator is equivariant under interest-respecting reparameterizations and is third-order median unbiased. With a vector parameter of interest, componentwise equivariance and third-order median centring are obtained. Like the implicit method of Firth (1993) for bias reduction, the new method does not require finiteness of the maximum likelihood estimate and is effective in preventing infinite estimates. Simulation results for continuous and discrete models, including binary and beta regression, confirm that the method succeeds in achieving componentwise median centring and in solving the boundary estimate problem, while keeping comparable dispersion and the same approximate distribution as its main competitors.

Suggested Citation

  • E C Kenne Pagui & A Salvan & N Sartori, 2017. "Median bias reduction of maximum likelihood estimates," Biometrika, Biometrika Trust, vol. 104(4), pages 923-938.
    • Handle: RePEc:oup:biomet:v:104:y:2017:i:4:p:923-938.
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    File URL: http://hdl.handle.net/10.1093/biomet/asx046
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    Cited by:

    1. Frederico Machado Almeida & Enrico Antônio Colosimo & Vinícius Diniz Mayrink, 2021. "Firth adjusted score function for monotone likelihood in the mixture cure fraction model," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(1), pages 131-155, January.
    2. Rigon, Tommaso & Aliverti, Emanuele, 2023. "Conjugate priors and bias reduction for logistic regression models," Statistics & Probability Letters, Elsevier, vol. 202(C).
    3. Manlio Migliorati & Marica Manisera & Paola Zuccolotto, 2023. "Integration of model-based recursive partitioning with bias reduction estimation: a case study assessing the impact of Oliver’s four factors on the probability of winning a basketball game," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 107(1), pages 271-293, March.

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