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Semiparametric Mixtures in Case-Control Studies

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  • Murphy, S. A.
  • van der Vaart, A. W.

Abstract

We consider likelihood based inference in a class of logistic models for case- control studies with a partially observed covariate. The likelihood is a combination of a nonparametric mixture, a parametric likelihood, and an empirical likelihood. We prove the asymptotic normality of the maximum likelihood estimator for the regression slope, the asymptotic chi-squared distribution of the likelihood ratio statistic, and the consistency of the observed information, in both the prospective and the retrospective model.

Suggested Citation

  • Murphy, S. A. & van der Vaart, A. W., 2001. "Semiparametric Mixtures in Case-Control Studies," Journal of Multivariate Analysis, Elsevier, vol. 79(1), pages 1-32, October.
    • Handle: RePEc:eee:jmvana:v:79:y:2001:i:1:p:1-32
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    References listed on IDEAS

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    1. A. W. van der Vaart, 1995. "Efficiency. of infinite dimensional M‐ estimators," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 49(1), pages 9-30, March.
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    Cited by:

    1. Zhiwei Zhang & Howard Rockette, 2006. "Semiparametric Maximum Likelihood for Missing Covariates in Parametric Regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(4), pages 687-706, December.
    2. Cheng, Guang & Kosorok, Michael R., 2009. "The penalized profile sampler," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 345-362, March.
    3. Guang Cheng, 2015. "Moment Consistency of the Exchangeably Weighted Bootstrap for Semiparametric M-estimation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(3), pages 665-684, September.
    4. Suhyun Kang & Wenbin Lu & Mengling Liu, 2017. "Efficient estimation for accelerated failure time model under case-cohort and nested case-control sampling," Biometrics, The International Biometric Society, vol. 73(1), pages 114-123, March.
    5. Alan Huang, 2013. "Density estimation and nonparametric inferences using maximum likelihood weighted kernels," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(3), pages 561-571, September.

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