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Empirical Likelihood Ratio in Terms of Cumulative Hazard Function for Censored Data

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  • Pan, Xiao-Rong
  • Zhou, Mai

Abstract

It has been shown that (with complete data) empirical likelihood ratios can be used to form confidence intervals and test hypotheses about a linear functional of the distribution function just like the parametric case. We study here the empirical likelihood ratios for right censored data and with parameters that are linear functionals of the cumulative hazard function. Martingale techniques make the asymptotic analysis easier, even for random weighting functions. It is shown that the empirical likelihood ratio in this setting can be easily obtained by solving a one parameter monotone equation.

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  • Pan, Xiao-Rong & Zhou, Mai, 2002. "Empirical Likelihood Ratio in Terms of Cumulative Hazard Function for Censored Data," Journal of Multivariate Analysis, Elsevier, vol. 80(1), pages 166-188, January.
    • Handle: RePEc:eee:jmvana:v:80:y:2002:i:1:p:166-188
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    1. Borm, Peter & Keiding, H & McLean, R.P. & Oortwijn, S & Tijs, S, 1992. "The Compromise Value for NTU-Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(2), pages 175-189.
    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.
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    Cited by:

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    2. Judith H. Parkinson, 2020. "Combined multiple testing of multivariate survival times by censored empirical likelihood," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(3), pages 757-786, September.
    3. Varron, Davit, 2016. "Empirical likelihood confidence tubes for functional parameters in plug-in estimation," Journal of Multivariate Analysis, Elsevier, vol. 152(C), pages 100-118.
    4. Hilmi Fadel Kittani, 2024. "Generalized k‐variate proportional hazard function for censored survival data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 78(3), pages 478-484, August.
    5. Bin Dong & David E. Matthews, 2012. "Empirical Likelihood for Cumulative Hazard Ratio Estimation with Covariate Adjustment," Biometrics, The International Biometric Society, vol. 68(2), pages 408-418, June.

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