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Empirical likelihood analysis of the Buckley-James estimator

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  • Zhou, Mai
  • Li, Gang

Abstract

The censored linear regression model, also referred to as the accelerated failure time (AFT) model when the logarithm of the survival time is used as the response variable, is widely seen as an alternative to the popular Cox model when the assumption of proportional hazards is questionable. Buckley and James [Linear regression with censored data, Biometrika 66 (1979) 429-436] extended the least squares estimator to the semiparametric censored linear regression model in which the error distribution is completely unspecified. The Buckley-James estimator performs well in many simulation studies and examples. The direct interpretation of the AFT model is also more attractive than the Cox model, as Cox has pointed out, in practical situations. However, the application of the Buckley-James estimation was limited in practice mainly due to its illusive variance. In this paper, we use the empirical likelihood method to derive a new test and confidence interval based on the Buckley-James estimator of the regression coefficient. A standard chi-square distribution is used to calculate the P-value and the confidence interval. The proposed empirical likelihood method does not involve variance estimation. It also shows much better small sample performance than some existing methods in our simulation studies.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:99:y:2008:i:4:p:649-664
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    References listed on IDEAS

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    1. 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.
    2. Li, Gang, 1995. "On nonparametric likelihood ratio estimation of survival probabilities for censored data," Statistics & Probability Letters, Elsevier, vol. 25(2), pages 95-104, November.
    3. 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.
    4. Zhezhen Jin & D. Y. Lin & Zhiliang Ying, 2006. "On least-squares regression with censored data," Biometrika, Biometrika Trust, vol. 93(1), pages 147-161, March.
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    Cited by:

    1. Han-Ying Liang & Jacobo Uña-Álvarez, 2012. "Empirical likelihood for conditional quantile with left-truncated and dependent data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(4), pages 765-790, August.
    2. 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.
    3. Zhao, Yichuan & Meng, Xueping & Yang, Hanfang, 2015. "Jackknife empirical likelihood inference for the mean absolute deviation," Computational Statistics & Data Analysis, Elsevier, vol. 91(C), pages 92-101.
    4. Mai Zhou & Yifan Yang, 2015. "A recursive formula for the Kaplan–Meier estimator with mean constraints and its application to empirical likelihood," Computational Statistics, Springer, vol. 30(4), pages 1097-1109, December.
    5. 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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