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Empirical likelihood inference for the accelerated failure time model

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  • Zhao, Yichuan
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    Abstract

    Accelerated failure time (AFT) models are useful regression tools for studying the association between a survival time and covariates. Semiparametric inference procedures have been proposed in an extensive literature. Among these, use of an estimating equation which is monotone in the regression parameter and has some excellent properties was proposed by Fygenson and Ritov (1994). However, there is a serious under-coverage problem for small sample sizes. In this paper, we derive the limiting distribution of the empirical log-likelihood ratio for the regression parameter on the basis of the monotone estimating equations. Furthermore, the empirical likelihood (EL) confidence intervals/regions for the regression parameter are obtained. We conduct a simulation study in order to compare the proposed EL method with the normal approximation method. The simulation results suggest that the empirical likelihood based method outperforms the normal approximation based method in terms of coverage probability. Thus, the proposed EL method overcomes the under-coverage problem of the normal approximation method.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 81 (2011)
    Issue (Month): 5 (May)
    Pages: 603-610

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    Handle: RePEc:eee:stapro:v:81:y:2011:i:5:p:603-610

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    Related research

    Keywords: Average length Confidence interval/region Coverage probability Monotone estimating equation Right censoring;

    References

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    1. 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.
    2. 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.
    3. Jing, Bing-Yi & Yuan, Junqing & Zhou, Wang, 2009. "Jackknife Empirical Likelihood," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 1224-1232.
    4. Jing, Bing-Yi & Yuan, Junqing & Zhou, Wang, 2008. "Empirical likelihood for non-degenerate U-statistics," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 599-607, April.
    5. Gengsheng Qin, 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.
    6. Mai Zhou, 2005. "Empirical likelihood analysis of the rank estimator for the censored accelerated failure time model," Biometrika, Biometrika Trust, vol. 92(2), pages 492-498, June.
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