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Weighted Empirical Likelihood Ratio Confidence Intervals for the Mean with Censored Data

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Abstract

We propose a procedure to construct the empirical likelihood ratio confidence interval for the mean using a resampling method. This approach leads to the definition of a likelihood function for censored data, called weighted empirical likelihood function. With the second order expansion of the log likelihood ratio, a weighted empirical likelihood ratio confidence interval for the mean is proposed and shown by simulation studies to have comparable coverage accuracy to alternative methods, including the nonparametric bootstrap-t. The procedures proposed here apply in a unified way to different types of censored data, such as right censored data, doubly censored data and interval censored data, and computationally more efficient than the bootstrap-t method. An example of a set of doubly censored breast cancer data is presented with the application of our methods.

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References

  • Chang, M. N. and Yang, G. L. (1987). Strong consistency of a nonparametric estimator of the survival function with doubly censored data, Ann. Statist., 15, 1536-1547.

    Google Scholar 

  • Chung, K. L. (1974). A Course in Probability Theory, Academic Press, New York.

    Google Scholar 

  • DiCiccio, T. J., Hall, P. J. and Romano, J. (1991). Empirical likelihood is Bartlettcorrectable, Ann. Statist., 19, 1053-1061.

    Google Scholar 

  • Efron, B. (1967). The two sample problem with censored data, Proc. Fifth Berkeley Symp. on Math. Statist. Prob., Vol.4, 831-853, University of California Press, Berkeley.

    Google Scholar 

  • Efron, B. and Tibshirani, R. J. (1993). An Introduction to the Bootstrap, Chapman & Hall, New York.

    Google Scholar 

  • Groeneboom, P. and Wellner, J. A. (1992). Information Bounds and Nonparametric Maximum Likelihood Estimation, Birkhäuser, Basel, Switzerland.

    Google Scholar 

  • Gu, M. G. and Zhang, C. H. (1993). Asymptotic properties of self-consistent estimators based on doubly censored data, Ann. Statist., 21, 611-624.

    Google Scholar 

  • Kim, M. Y., De Gruttola, V. G. and Lagakos, S. W. (1993). Analyzing doubly censored data with covariates, with application to AIDS, Biometrics, 49, 13-22.

    Google Scholar 

  • Miller, R. G. (1976). Least squared regression with censored data, Biometrika, 63, 449-464.

    Google Scholar 

  • Mykland, P. A. (1995). Dual likelihood, Ann. Statist., 23, 396-421.

    Google Scholar 

  • Mykland, P. A. and Ren, J. (1996). Algorithms for computing self-consistent and maximum likelihood estimators with doubly censored data, Ann. Statist., 24, 1740-1764.

    Google Scholar 

  • Owen, A. B. (1988). Empirical likelihood ratio confidence intervals for a single functional, Biometrika, 75, 237-249.

    Google Scholar 

  • Owen, A. B. (1990). Empirical likelihood ratio confidence regions, Ann. Statist., 18, 90-120.

    Google Scholar 

  • Owen, A. B. (1991). Empirical likelihood for linear models, Ann. Statist., 19, 1725-1747.

    Google Scholar 

  • Peer, P. G., Van Dijck, J. A., Hendriks, J. H., Holland, R. and Verbeek, A. L. (1993). Age-dependent growth rate of primary breast cancer, Cancer, Jun 1–71(11), 3547-3551.

    Google Scholar 

  • Qin, J. and Lawless, J. F. (1994). Empirical likelihood and general estimating equations, Ann. Statist., 22, 300-325.

    Google Scholar 

  • Ren, J. (1995a). Generalized Cramér-von Mises tests of goodness of fit for doubly censored data, Ann. Inst. Statist. Math., 47, 525-549.

    Google Scholar 

  • Ren, J. (1995b). Self-consistent estimators, bootstrap and censored data, IMB Bulletin, 24(5), p. 467.

    Google Scholar 

  • Ren, J. and Peer, P. G. (2000). A study on effectiveness of screening mammograms, International Journal of Epidemiology, 29, 803-806.

    Google Scholar 

  • Shorack, R. G. and Wellner, J. A. (1986). Empirical Processes with Applications to Statistics, Wiley, New York.

    Google Scholar 

  • Stute, W. and Wang, J. L. (1993). The strong law under random censorship, Ann. Statist., 21, 1591-1607.

    Google Scholar 

  • Turnbull, B. W. (1974). Nonparametric estimation of a survivorship function with doubly censored data, J. Amer. Statist. Assoc., 69, 169-173.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Tulane University, New Orleans, LA, 70118, USA

    Jian-Jian Ren

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  1. Jian-Jian Ren
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Ren, JJ. Weighted Empirical Likelihood Ratio Confidence Intervals for the Mean with Censored Data. Annals of the Institute of Statistical Mathematics 53, 498–516 (2001). https://doi.org/10.1023/A:1014612911961

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