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Empirical likelihood inference for censored median regression model via nonparametric kernel estimation

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  • Zhao, Yichuan
  • Chen, Feiming
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    Abstract

    An alternative to the accelerated failure time model is to regress the median of the failure time on the covariates. In the recent years, censored median regression models have been shown to be useful for analyzing a variety of censored survival data with the robustness property. Based on missing information principle, a semiparametric inference procedure for regression parameter has been developed when censoring variable depends on continuous covariate. In order to improve the low coverage accuracy of such procedure, we apply an empirical likelihood ratio method (EL) to the model and derive the limiting distributions of the estimated and adjusted empirical likelihood ratios for the vector of regression parameter. Two kinds of EL confidence regions for the unknown vector of regression parameters are obtained accordingly. We conduct an extensive simulation study to compare the performance of the proposed methods with that normal approximation based method. The simulation results suggest that the EL methods outperform the normal approximation based method in terms of coverage probability. Finally, we make some discussions about our methods.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 99 (2008)
    Issue (Month): 2 (February)
    Pages: 215-231

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    Handle: RePEc:eee:jmvana:v:99:y:2008:i:2:p:215-231

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    Related research

    Keywords: Confidence regions Conditional Nelson-Aalen estimator Coverage probability Least absolute deviations Right censoring;

    References

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    1. Stute, Winfried & Xue, Liugen & Zhu, Lixing, 2007. "Empirical Likelihood Inference in Nonlinear Errors-in-Covariables Models With Validation Data," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 332-346, March.
    2. Glenn, N.L. & Zhao, Yichuan, 2007. "Weighted empirical likelihood estimates and their robustness properties," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 5130-5141, June.
    3. Jing Qin & Biao Zhang, 2007. "Empirical-likelihood-based inference in missing response problems and its application in observational studies," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(1), pages 101-122.
    4. Song Chen, 1993. "On the accuracy of empirical likelihood confidence regions for linear regression model," Annals of the Institute of Statistical Mathematics, Springer, vol. 45(4), pages 621-637, December.
    5. Lai, Tze Leung & Ying, Zhiliang, 1992. "Linear rank statistics in regression analysis with censored or truncated data," Journal of Multivariate Analysis, Elsevier, vol. 40(1), pages 13-45, January.
    6. 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.
    7. McKeague, Ian W. & Zhao, Yichuan, 2006. "Width-scaled confidence bands for survival functions," Statistics & Probability Letters, Elsevier, vol. 76(4), pages 327-339, February.
    8. Wang, Qi-Hua & Jing, Bing-Yi, 1999. "Empirical likelihood for partial linear models with fixed designs," Statistics & Probability Letters, Elsevier, vol. 41(4), pages 425-433, February.
    9. Shi, Jian & Lau, Tai-Shing, 2000. "Empirical Likelihood for Partially Linear Models," Journal of Multivariate Analysis, Elsevier, vol. 72(1), pages 132-148, January.
    10. 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.
    11. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    12. Chen, S. X., 1994. "Empirical Likelihood Confidence Intervals for Linear Regression Coefficients," Journal of Multivariate Analysis, Elsevier, vol. 49(1), pages 24-40, April.
    13. Qihua Wang, 2002. "Empirical Likelihood-based Inference in Linear Models with Missing Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 29(3), pages 563-576.
    14. Einmahl, J.H.J. & McKeague, I.W., 1999. "Confidence tubes for multiple quantile plots via empirical likelihood," Open Access publications from Tilburg University urn:nbn:nl:ui:12-142078, Tilburg University.
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    Cited by:
    1. Yichuan Zhao & Ali Jinnah, 2012. "Inference for Cox’s regression models via adjusted empirical likelihood," Computational Statistics, Springer, vol. 27(1), pages 1-12, March.
    2. Zhao, Yichuan, 2010. "Semiparametric inference for transformation models via empirical likelihood," Journal of Multivariate Analysis, Elsevier, vol. 101(8), pages 1846-1858, September.
    3. Gong, Yun & Peng, Liang & Qi, Yongcheng, 2010. "Smoothed jackknife empirical likelihood method for ROC curve," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1520-1531, July.

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