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Empirical Likelihood for Censored Linear Regression

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  • Gengsheng Qin
  • Bing‐Yi Jing

Abstract

In this paper we investigate the empirical likelihood method in a linear regression model when the observations are subject to random censoring. An empirical likelihood ratio for the slope parameter vector is defined and it is shown that its limiting distribution is a weighted sum of independent chi‐square distributions. This reduces to the empirical likelihood to the linear regression model first studied by Owen (1991) if there is no censoring present. Some simulation studies are presented to compare the empirical likelihood method with the normal approximation based method proposed in Lai et al. (1995). It was found that the empirical likelihood method performs much better than the normal approximation method.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:scjsta:v:28:y:2001:i:4:p:661-673
    DOI: 10.1111/1467-9469.00261
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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. Song Chen & Ingrid Van Keilegom, 2009. "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 415-447, November.
    3. Yongcheng Qi, 2010. "On the tail index of a heavy tailed distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(2), pages 277-298, April.
    4. 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.
    5. Jonker Marianne & Van der Vaart Aad, 2014. "On the Correction of the Asymptotic Distribution of the Likelihood Ratio Statistic If Nuisance Parameters Are Estimated Based on an External Source," The International Journal of Biostatistics, De Gruyter, vol. 10(2), pages 123-142, November.
    6. Zhou, Mai & Li, Gang, 2008. "Empirical likelihood analysis of the Buckley-James estimator," Journal of Multivariate Analysis, Elsevier, vol. 99(4), pages 649-664, April.
    7. Tong Tong Wu & Gang Li & Chengyong Tang, 2015. "Empirical Likelihood for Censored Linear Regression and Variable Selection," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(3), pages 798-812, September.
    8. 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.
    9. Yongli Sang, 2021. "A Jackknife Empirical Likelihood Approach for Testing the Homogeneity of K Variances," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(7), pages 1025-1048, October.
    10. Gang Li & Xuyang Lu, 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 463-467, November.
    11. Wen Yu & Yunting Sun & Ming Zheng, 2011. "Empirical likelihood method for linear transformation models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(2), pages 331-346, April.
    12. Zhao, Yichuan, 2011. "Empirical likelihood inference for the accelerated failure time model," Statistics & Probability Letters, Elsevier, vol. 81(5), pages 603-610, May.

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