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Empirical likelihood inference for median regression models for censored survival data

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  • Qin, Gengsheng
  • Tsao, Min

Abstract

Recent advances in median regression model have made it possible to use this model for analyzing a variety of censored survival data. For inference on the model parameter vector, there are now semiparametric procedures based on normal approximation that are valid without strong conditions on the error distribution. However, the accuracy of such procedures can be quite low when the censoring proportion is high. In this paper, we propose an alternative semiparametric procedure based on the empirical likelihood. We define the empirical likelihood ratio for the parameter vector and show that its limiting distribution is a weighted sum of chi-square distributions. Numerical results from a simulation study suggest that the empirical likelihood method is more accurate than the normal approximation based method of Ying et al. (J. Amer. Statist. Assoc. 90 (1995) 178).

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  • 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.
    • Handle: RePEc:eee:jmvana:v:85:y:2003:i:2:p:416-430
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    Cited by:

    1. 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.
    2. Tang, Cheng Yong & Leng, Chenlei, 2012. "An empirical likelihood approach to quantile regression with auxiliary information," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 29-36.
    3. Shim, Jooyong & Hwang, Changha, 2009. "Support vector censored quantile regression under random censoring," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 912-919, February.
    4. 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.
    5. Ould-SaI¨d, Elias, 2006. "A strong uniform convergence rate of kernel conditional quantile estimator under random censorship," Statistics & Probability Letters, Elsevier, vol. 76(6), pages 579-586, March.
    6. Yichuan Zhao & Song Yang, 2008. "Empirical likelihood inference for censored median regression with weighted empirical hazard functions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(2), pages 441-457, June.
    7. Xiaofeng Lv & Gupeng Zhang & Xinkuo Xu & Qinghai Li, 2017. "Bootstrap-calibrated empirical likelihood confidence intervals for the difference between two Gini indexes," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 15(2), pages 195-216, June.
    8. Ming Zheng & Wen Yu, 2013. "Empirical likelihood method for multivariate Cox regression," Computational Statistics, Springer, vol. 28(3), pages 1241-1267, June.
    9. Han-Ying Liang & Jacobo Uña-Álvarez, 2011. "Asymptotic properties of conditional quantile estimator for censored dependent observations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(2), pages 267-289, April.
    10. Zhong, Pingshou & Cui, Hengjian, 2010. "Empirical likelihood for median regression model with designed censoring variables," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 240-251, January.
    11. Sundarraman Subramanian, 2020. "Function-based hypothesis testing in censored two-sample location-scale models," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(1), pages 183-213, January.
    12. Gengsheng Qin & Xiao-Hua Zhou, 2006. "Empirical Likelihood Inference for the Area under the ROC Curve," Biometrics, The International Biometric Society, vol. 62(2), pages 613-622, June.
    13. Xiaofeng Lv & Rui Li, 2013. "Smoothed empirical likelihood analysis of partially linear quantile regression models with missing response variables," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 97(4), pages 317-347, October.
    14. Zhangong Zhou & Rong Jiang & Weimin Qian, 2013. "LAD variable selection for linear models with randomly censored data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(2), pages 287-300, February.
    15. Bravo, Francesco, 2009. "Two-step generalised empirical likelihood inference for semiparametric models," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1412-1431, August.
    16. Guo-Liang Fan & Han-Ying Liang & Zhen-Sheng Huang, 2012. "Empirical likelihood for partially time-varying coefficient models with dependent observations," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(1), pages 71-84.
    17. César Sánchez-Sellero, 2009. "Comments on: A review on empirical likelihood methods for regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(3), pages 458-460, November.
    18. Tang, Linjun & Zhou, Zhangong & Wu, Changchun, 2012. "Weighted composite quantile estimation and variable selection method for censored regression model," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 653-663.
    19. Qibing Gao & Xiuqing Zhou & Yanqin Feng & Xiuli Du & XiaoXiao Liu, 2021. "An empirical likelihood method for quantile regression models with censored data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(1), pages 75-96, January.
    20. Xiaofeng Lv & Gupeng Zhang & Xinkuo Xu & Qinghai Li, 2017. "Bootstrap-calibrated empirical likelihood confidence intervals for the difference between two Gini indexes," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 15(2), pages 195-216, June.
    21. Yu Shen & Han-Ying Liang, 2018. "Quantile regression and its empirical likelihood with missing response at random," Statistical Papers, Springer, vol. 59(2), pages 685-707, June.
    22. Lu, Wenbin & Liang, Yu, 2006. "Empirical likelihood inference for linear transformation models," Journal of Multivariate Analysis, Elsevier, vol. 97(7), pages 1586-1599, August.
    23. Zhao, Yichuan & Chen, Feiming, 2008. "Empirical likelihood inference for censored median regression model via nonparametric kernel estimation," Journal of Multivariate Analysis, Elsevier, vol. 99(2), pages 215-231, February.

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