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Inference for the Mean Difference in the Two-Sample Random Censorship Model

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  • Wang, Qihua
  • Wang, Jane-Ling

Abstract

Inference for the mean difference in the two-sample random censorship model is an important problem in comparative survival and reliability test studies. This paper develops an adjusted empirical likelihood inference and a martingale-based bootstrap inference for the mean difference. A nonparametric version of Wilks' theorem for the adjusted empirical likelihood is derived, and the corresponding empirical likelihood confidence interval of the mean difference is constructed. Also, it is shown that the martingale-based bootstrap gives a correct first order asymptotic approximation of the corresponding estimator of the mean difference, which ensures that the martingale-based bootstrap confidence interval has asymptotically correct coverage probability. A simulation study is conducted to compare the adjusted empirical likelihood, the martingale-based bootstrap, and Efron's bootstrap in terms of coverage accuracies and average lengths of the confidence intervals. The simulation indicates that the proposed adjusted empirical likelihood and the martingale-based bootstrap confidence procedures are comparable, and both seem to outperform Efron's bootstrap procedure.

Suggested Citation

  • Wang, Qihua & Wang, Jane-Ling, 2001. "Inference for the Mean Difference in the Two-Sample Random Censorship Model," Journal of Multivariate Analysis, Elsevier, vol. 79(2), pages 295-315, November.
    • Handle: RePEc:eee:jmvana:v:79:y:2001:i:2:p:295-315
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    References listed on IDEAS

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    1. Jing Qin, 1994. "Semi-empirical likelihood ratio confidence intervals for the difference of two sample means," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(1), pages 117-126, March.
    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. Wang, Qi-Hua & Jing, Bing-Yi, 1999. "Empirical likelihood for partial linear models with fixed designs," Statistics & Probability Letters, Elsevier, vol. 41(4), pages 425-433, February.
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    Cited by:

    1. 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.
    2. Shen, Junshan & Yuen, Kam Chuen & Liu, Chunling, 2016. "Empirical likelihood confidence regions for one- or two- samples with doubly censored data," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 285-293.
    3. 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.
    4. Zhou, Mai & Zhu, Shihong, 2015. "Empirical likelihood confidence band for the difference of survival functions under proportional hazards model," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 228-235.

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