Empirical Bayes Estimation with Random Censoring

  • TaChen LiangEmail author


We study empirical Bayes estimation for exponential distributions based on randomly censored data. An empirical Bayes estimator φ̃n is constructed. The rate of asymptotic optimality of φ̃n is investigated. It is shown that under certain conditions, the regret of φ̃n converges to zero at a rate O(ln4n/n1/2), where n is the number of past data available when the present estimation problem is considered.

AMS Subject Classification



Kaplan-Meier estimator Random censoring Rate of convergence Regret 


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  1. Bitouze, D., Laurent, B., Massart, P., 1999. A Dvoretzky-Kiefer-Wolfowitz type inequality for the Kaplan-Meier estimator. Ann. Inst. Henri Poincare, 35, 735–763.MathSciNetCrossRefGoogle Scholar
  2. Gradshteyn, I. S., Ryzhik, I. M., 1994. Tables of Integrals, Series and Products. 5th edition, Academic Press, New York.zbMATHGoogle Scholar
  3. Liang, T., 2004. Empirical Bayes estimation with random right censoring. International J. Information and Management Sciences, 15(4), 1–12.MathSciNetzbMATHGoogle Scholar
  4. Liang, T., 2006. Empirical Bayes testing with exponential random right censoring. International J. Information and Management Sciences, 17(2), 71–84.MathSciNetzbMATHGoogle Scholar
  5. Liang, T., 2009. Empirical Bayes estimation of θ b in positive exponential families. J. Statist. Plann. & Inferences, 139, 411–424.MathSciNetCrossRefGoogle Scholar
  6. Pensky, M., Singh, R. S., 1999. Empirical Bayes estimation of reliability characteristics for an exponential family. Canadian J. Statist., 27, 127–136.MathSciNetCrossRefGoogle Scholar
  7. Robbins, H., 1956. An empirical Bayes approach to statistics. Proc. Third Berkeley Symp. Math. Statist. and Probab., University of California Press, Berkeley, CA, Vol. 1, 157–163.MathSciNetzbMATHGoogle Scholar
  8. Singh, R. S., 1979. Empirical Bayes estimation in Lebesgue-exponential families with rates near the best possible rate. Ann. Statist., 7, 890–902.MathSciNetCrossRefGoogle Scholar
  9. Susarla, V., van Ryzin, J., 1978. Empirical Bayes estimation of a distribution (survival) function from right censored observations. Ann. Statist., 6, 740–754.MathSciNetCrossRefGoogle Scholar
  10. Susarla, V., van Ryzin, J., 1986. Empirical Bayes procedures with censored data. In Adaptive Statistical Procedures and Related Topics, van Ryzin, J. (editor), IMS Lecture Notes-Monograph Series, Vol. 8, 219–234.MathSciNetCrossRefGoogle Scholar
  11. Wang, L., 2006a. Asymptotical optimality of empirical Bayes estimation under random censorship. (Chinese) Acta Math. Sci. Ser. A Chin. Ed., 26(6), 938–947.MathSciNetzbMATHGoogle Scholar
  12. Wang, L., 2006b. Empirical Bayes test for life parameter based on right censored data. Tamsui Oxf. J. Math. Sci., 22(2), 209–219.MathSciNetzbMATHGoogle Scholar
  13. Wang, L., Wang, Q., 2006. Empirical Bayes estimation under random censorship. Southeast Asian Bull. Math., 30(4), 779–788.MathSciNetzbMATHGoogle Scholar

Copyright information

© Grace Scientific Publishing 2010

Authors and Affiliations

  1. 1.Department of MathematicsWayne State UniversityDetroitUSA

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