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Minimum distance estimation for the logistic regression model


  • Howard D. Bondell


It is well known that the maximum likelihood fit of the logistic regression parameters can be greatly affected by atypical observations. Several robust alternatives have been proposed. However, if we consider the model from the case-control viewpoint, it is clear that current techniques can exhibit poor behaviour in many common situations. A new robust class of estimation procedures is introduced. The estimators are constructed via a minimum distance approach after identifying the model with a semiparametric biased sampling model. The approach is developed under the case-control sampling scheme, yet is shown to be applicable under prospective sampling as well. A weighted Cramer--von Mises distance is used as an illustrative example of the methodology. Copyright 2005, Oxford University Press.

Suggested Citation

  • Howard D. Bondell, 2005. "Minimum distance estimation for the logistic regression model," Biometrika, Biometrika Trust, vol. 92(3), pages 724-731, September.
  • Handle: RePEc:oup:biomet:v:92:y:2005:i:3:p:724-731

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    References listed on IDEAS

    1. Kai-tai Fang & Rahul Mukerjee, 2005. "Expected lengths of confidence intervals based on empirical discrepancy statistics," Biometrika, Biometrika Trust, vol. 92(2), pages 499-503, June.
    2. Whitney K. Newey & Richard J. Smith, 2004. "Higher Order Properties of Gmm and Generalized Empirical Likelihood Estimators," Econometrica, Econometric Society, vol. 72(1), pages 219-255, January.
    3. Kai-Tai Fang & Rahul Mukerjee, 2006. "Empirical-type likelihoods allowing posterior credible sets with frequentist validity: Higher-order asymptotics," Biometrika, Biometrika Trust, vol. 93(3), pages 723-733, September.
    4. Nicole A. Lazar, 2003. "Bayesian empirical likelihood," Biometrika, Biometrika Trust, vol. 90(2), pages 319-326, June.
    5. T. J. Sweeting, 1999. "On the construction of Bayes-confidence regions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(4), pages 849-861.
    6. Francesco Bravo, 2003. "Second-order power comparisons for a class of nonparametric likelihood-based tests," Biometrika, Biometrika Trust, vol. 90(4), pages 881-890, December.
    7. Susanne M. Schennach, 2005. "Bayesian exponentially tilted empirical likelihood," Biometrika, Biometrika Trust, vol. 92(1), pages 31-46, March.
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    Cited by:

    1. Bianco, Ana M. & Martínez, Elena, 2009. "Robust testing in the logistic regression model," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4095-4105, October.
    2. Geng, Pei & Sakhanenko, Lyudmila, 2016. "Parameter estimation for the logistic regression model under case-control study," Statistics & Probability Letters, Elsevier, vol. 109(C), pages 168-177.

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