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Minimum Hellinger distance estimation for a two-sample semiparametric cure rate model with censored survival data

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  • Yayuan Zhu
  • Jingjing Wu
  • Xuewen Lu

Abstract

Efficiency and robustness are two essential concerns on statistical estimation. Unfortunately, it was widely accepted that there existed a contradiction between achieving efficiency and robustness simultaneously. For parametric models with complete data, the minimum Hellinger distance estimation introduced by Beran (Ann Stat 5:445–463, 1977 ) has been shown that it can reconcile this contradiction. Because data in biostatistics, actuarial science or economics are often subject to censoring and even involve a fraction of long-term survivors, our study aims to extend the minimum Hellinger distance estimation to a two-sample semiparametric cure rate model with right-censored survival data. The asymptotic properties such as consistency, efficiency, normality, and robustness of the proposed estimator have been considered and its performances are examined via simulation studies in comparison with those of the maximum semiparametric conditional likelihood estimator introduced by Shen et al. (J Am Stat Assoc 102:1235–1244, 2007 ). Finally, our method is illustrated by analyzing a real data set: Bone Marrow Transplant Data. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Yayuan Zhu & Jingjing Wu & Xuewen Lu, 2013. "Minimum Hellinger distance estimation for a two-sample semiparametric cure rate model with censored survival data," Computational Statistics, Springer, vol. 28(6), pages 2495-2518, December.
    • Handle: RePEc:spr:compst:v:28:y:2013:i:6:p:2495-2518
    DOI: 10.1007/s00180-013-0416-7
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    References listed on IDEAS

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    1. Shen, Yu & Qin, Jing & Costantino, Joseph P., 2007. "Inference of Tamoxifen's Effects on Prevention of Breast Cancer From a Randomized Controlled Trial," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1235-1244, December.
    2. Woo, Mi-Ja & Sriram, T.N., 2006. "Robust Estimation of Mixture Complexity," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1475-1486, December.
    3. John P. Klein & Per Kragh Andersen, 2005. "Regression Modeling of Competing Risks Data Based on Pseudovalues of the Cumulative Incidence Function," Biometrics, The International Biometric Society, vol. 61(1), pages 223-229, March.
    4. Diehl, Sabine & Stute, Winfried, 1988. "Kernel density and hazard function estimation in the presence of censoring," Journal of Multivariate Analysis, Elsevier, vol. 25(2), pages 299-310, May.
    5. Wu, Jingjing & Karunamuni, Rohana & Zhang, Biao, 2010. "Minimum Hellinger distance estimation in a two-sample semiparametric model," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1102-1122, May.
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    Cited by:

    1. Max Wornowizki & Roland Fried, 2016. "Two-sample homogeneity tests based on divergence measures," Computational Statistics, Springer, vol. 31(1), pages 291-313, March.

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