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Asymptotically efficient estimation under semi-parametric random censorship models

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  • Dikta, Gerhard

Abstract

We study the estimation of some linear functionals which are based on an unknown lifetime distribution. The observations are assumed to be generated under the semi-parametric random censorship model (SRCM), that is, a random censorship model where the conditional expectation of the censoring indicator given the observation belongs to a parametric family. Under this setup a semi-parametric estimator of the survival function was introduced by the author. If the parametric model assumption is correct, it is known that the estimated functional which is based on this semi-parametric estimator is asymptotically at least as efficient as the corresponding one which rests on the nonparametric Kaplan–Meier estimator.

Suggested Citation

  • Dikta, Gerhard, 2014. "Asymptotically efficient estimation under semi-parametric random censorship models," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 10-24.
    • Handle: RePEc:eee:jmvana:v:124:y:2014:i:c:p:10-24
    DOI: 10.1016/j.jmva.2013.10.002
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    References listed on IDEAS

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    1. Subramanian, Sundarraman, 2011. "Multiple imputations and the missing censoring indicator model," Journal of Multivariate Analysis, Elsevier, vol. 102(1), pages 105-117, January.
    2. Yang, Song, 1990. "Efficient robust estimation of parameter in the random censorship model," Statistics & Probability Letters, Elsevier, vol. 10(5), pages 419-426, October.
    3. Sun, Liuquan & Zhu, Lixing, 2000. "A semiparametric model for truncated and censored data," Statistics & Probability Letters, Elsevier, vol. 48(3), pages 217-227, July.
    4. Dikta, Gerhard & Kvesic, Marsel & Schmidt, Christian, 2006. "Bootstrap Approximations in Model Checks for Binary Data," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 521-530, June.
    5. Schick A. & Susarla V. & Koul H., 1988. "Efficient Estimation Of Functionals With Censored Data," Statistics & Risk Modeling, De Gruyter, vol. 6(4), pages 349-360, April.
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    Cited by:

    1. Nubyra Ahmed & Sundarraman Subramanian, 2016. "Semiparametric simultaneous confidence bands for the difference of survival functions," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 22(4), pages 504-530, October.
    2. Bhattacharya, Rianka & Subramanian, Sundarraman, 2014. "Two-sample location–scale estimation from semiparametric random censorship models," Journal of Multivariate Analysis, Elsevier, vol. 132(C), pages 25-38.
    3. Dikta, Gerhard & Reißel, Martin & Harlaß, Carsten, 2016. "Semi-parametric survival function estimators deduced from an identifying Volterra type integral equation," Journal of Multivariate Analysis, Elsevier, vol. 147(C), pages 273-284.
    4. Subramanian, Sundarraman, 2016. "Bootstrap likelihood ratio confidence bands for survival functions under random censorship and its semiparametric extension," Journal of Multivariate Analysis, Elsevier, vol. 147(C), pages 58-81.
    5. Shoubhik Mondal & Sundarraman Subramanian, 2016. "Simultaneous confidence bands for Cox regression from semiparametric random censorship," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 22(1), pages 122-144, January.

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