Abstract
The empirical likelihood was introduced by Owen, although its idea originated from survival analysis in the context of estimating the survival probabilities given by Thomas and Grunkemeier. In this paper, we investigate how to apply the empirical likelihood method to a class of functionals of survival function in the presence of censoring. We define an adjusted empirical likelihood and show that it follows a chi-square distribution. Some simulation studies are presented to compare the empirical likelihood method with the Studentized-t method. These results indicate that the empirical likelihood method works better than or equally to the Studentized-t method, depending on the situations.
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References
Chen, S. X. (1993). On the accuracy of empirical likelihood confidence regions for linear regression model, Ann. Inst. Statist. Math., 45, 621-637.
Chen, S. X. (1994). Empirical likelihood confidence intervals for linear regression coefficients. J. Multivariate Anal., 49, 24-40.
DiCiccio, T. J., Hall, P. and Romano, J. P. (1991). Bartlett adjustment for empirical likelihood, Ann. Statist., 19, 1053-1061.
Hall, P. and La Scala, B. (1990). Methodology and algorithms of empirical likelihood, International Statistical Review, 58(2), 109-127.
Li, G. (1995). On nonparametric likelihood ratio estimation of survival probabilities for censored data, Statist. Probab. Lett., 90, 95-104.
Murphy, S. A. (1995). Likelihood-ratio based confidence intervals in survival analysis, J. Amer. Statist. Assoc., 90, 1399-1405.
Owen, A. (1988). Empirical likelihood ratio confidence intervals for single functional, Biometrika, 75, 237-249.
Owen, A. (1990). Empirical likelihood ratio confidence regions, Ann. Statist., 18, 90-120.
Qin, J. and Lawless, J. F. (1994). Empirical likelihood and general estimating equations, Ann. Statist., 22, 300-325.
Stute, W. (1995). The central limit theorem under random censorship, Ann. Statist., 23, 422-439.
Stute, W. (1996). The jackknife estimate of variance of a Kaplan-Meier integral, Ann. Statist., 24, 2679-2704.
Stute, W. and Wang, J.-L. (1993). The strong law under random censorship, Ann. Statist., 21, 1591-1607.
Thomas, D. R. and Grunkemeier, G. L. (1975). Confidence interval estimation of survival probabilities for censored data, J. Amer. Statist. Assoc., 70, 865-871.
Zhou, M. (1992). Asymptotic normality of the synthetic estimator for censored survival data, Ann. Statist., 20, 1002-1021.
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Wang, QH., Jing, BY. Empirical Likelihood for a Class of Functionals of Survival Distribution with Censored Data. Annals of the Institute of Statistical Mathematics 53, 517–527 (2001). https://doi.org/10.1023/A:1014617112870
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DOI: https://doi.org/10.1023/A:1014617112870