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Empirical likelihood inference for the mean residual life under random censorship

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  • Qin, Gengsheng
  • Zhao, Yichuan

Abstract

Mean residual life (MRL) for a lifetime random variable X is one of the basic parameters of interest in survival analysis. There has been a lot of work available on the inference of MRL in the complete data setting. However, the observations for X are often censored. Inference for MRL becomes more involved under random censorship. In this paper, an empirical likelihood procedure is proposed for the inference of MRL with right censored data. It is shown that the limiting distribution of the empirical log-likelihood ratio for MRL is a scaled chi-square distribution. The limiting distribution can be used to construct empirical likelihood-based confidence intervals for MRL. Numerical results from a simulation study suggest that the empirical likelihood-based confidence intervals have better coverage accuracy than the existing normal approximation-based confidence intervals.

Suggested Citation

  • Qin, Gengsheng & Zhao, Yichuan, 2007. "Empirical likelihood inference for the mean residual life under random censorship," Statistics & Probability Letters, Elsevier, vol. 77(5), pages 549-557, March.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:5:p:549-557
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    References listed on IDEAS

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    1. Qin, Gengsheng & Jing, Bing-Yi, 2001. "Censored Partial Linear Models and Empirical Likelihood," Journal of Multivariate Analysis, Elsevier, vol. 78(1), pages 37-61, July.
    2. Qin, Gengsheng & Tsao, Min, 2003. "Empirical likelihood inference for median regression models for censored survival data," Journal of Multivariate Analysis, Elsevier, vol. 85(2), pages 416-430, May.
    3. McKeague, Ian W. & Zhao, Yichuan, 2002. "Simultaneous confidence bands for ratios of survival functions via empirical likelihood," Statistics & Probability Letters, Elsevier, vol. 60(4), pages 405-415, December.
    4. Song Chen, 1993. "On the accuracy of empirical likelihood confidence regions for linear regression model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(4), pages 621-637, December.
    5. Gengsheng Qin & Bing‐Yi Jing, 2001. "Empirical Likelihood for Censored Linear Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(4), pages 661-673, December.
    6. Gianfranco Adimari, 1997. "Empirical Likelihood Type Confidence Intervals Under Random Censorship," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(3), pages 447-466, September.
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    Cited by:

    1. Jiayin Zheng & Junshan Shen & Shuyuan He, 2014. "Adjusted empirical likelihood for right censored lifetime data," Statistical Papers, Springer, vol. 55(3), pages 827-839, August.
    2. Junshan Shen & Wei Liang & Shuyuan He, 2012. "Likelihood ratio inference for mean residual life," Statistical Papers, Springer, vol. 53(2), pages 401-408, May.

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