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Parameter estimation for the logistic regression model under case-control study

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  • Geng, Pei
  • Sakhanenko, Lyudmila

Abstract

The article proposes parameter estimation and model testing of logistic regressions under case-control framework. Estimators are proposed by minimizing the integrated square distance (ISD) based on estimated density log-ratio. Estimation consistency and asymptotic normality are established. The test statistic based on the minimized ISD is also asymptotically normal under null hypotheses.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:109:y:2016:i:c:p:168-177
    DOI: 10.1016/j.spl.2015.11.019
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    References listed on IDEAS

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    1. Howard D. Bondell, 2005. "Minimum distance estimation for the logistic regression model," Biometrika, Biometrika Trust, vol. 92(3), pages 724-731, September.
    2. Howard D. Bondell, 2007. "Testing goodness-of-fit in logistic case-control studies," Biometrika, Biometrika Trust, vol. 94(2), pages 487-495.
    3. Xu Liu & Hongmei Jiang & Yong Zhou, 2014. "Local Empirical Likelihood Inference for Varying-Coefficient Density-Ratio Models Based on Case-Control Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(506), pages 635-646, June.
    4. Ganggang Xu & Suojin Wang, 2011. "A goodness-of-fit test of logistic regression models for case-control data with measurement error," Biometrika, Biometrika Trust, vol. 98(4), pages 877-886.
    5. Hall, Peter, 1984. "Central limit theorem for integrated square error of multivariate nonparametric density estimators," Journal of Multivariate Analysis, Elsevier, vol. 14(1), pages 1-16, February.
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