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Empirical likelihood inference for linear transformation models

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  • Lu, Wenbin
  • Liang, Yu

Abstract

Empirical likelihood inference is developed for censored survival data under the linear transformation models, which generalize Cox's [Regression models and life tables (with Discussion), J. Roy. Statist. Soc. Ser. B 34 (1972) 187-220] proportional hazards model. We show that the limiting distribution of the empirical likelihood ratio is a weighted sum of standard chi-squared distribution. Empirical likelihood ratio tests for the regression parameters with and without covariate adjustments are also derived. Simulation studies suggest that the empirical likelihood ratio tests are more accurate (under the null hypothesis) and powerful (under the alternative hypothesis) than the normal approximation based tests of Chen et al. [Semiparametric of transformation models with censored data, Biometrika 89 (2002) 659-668] when the model is different from the proportional hazards model and the proportion of censoring is high.

Suggested Citation

  • Lu, Wenbin & Liang, Yu, 2006. "Empirical likelihood inference for linear transformation models," Journal of Multivariate Analysis, Elsevier, vol. 97(7), pages 1586-1599, August.
  • Handle: RePEc:eee:jmvana:v:97:y:2006:i:7:p:1586-1599
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    References listed on IDEAS

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    1. 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.
    2. Chen, S. X., 1994. "Empirical Likelihood Confidence Intervals for Linear Regression Coefficients," Journal of Multivariate Analysis, Elsevier, vol. 49(1), pages 24-40, April.
    3. 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.
    4. Kani Chen, 2002. "Semiparametric analysis of transformation models with censored data," Biometrika, Biometrika Trust, vol. 89(3), pages 659-668, August.
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    Cited by:

    1. Ming Zheng & Wen Yu, 2013. "Empirical likelihood method for multivariate Cox regression," Computational Statistics, Springer, vol. 28(3), pages 1241-1267, June.
    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. 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.
    4. Bravo, Francesco, 2009. "Two-step generalised empirical likelihood inference for semiparametric models," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1412-1431, August.

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