Journal of the Korean Statistical Society

The Korean Statistical Society (한국통계학회)
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Empirical Bayes Nonparametric Estimation with Beta Processes Based on Censored Observations

  • Hong, Jee-Chang (Department of Liberal Arts, Dong Hae University) ;
  • Kim, Yongdai (Department of Statistics, Hankuk University of Foreign Studies) ;
  • Inha Jung (Division of Information and Computer Engineering, Ajou University)
  • Published : 2001.09.01
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Abstract

Empirical Bayes procedure of nonparametric estiamtion of cumulative hazard rates based on censored data is considered using the beta process priors of Hjort(1990). Beta process priors with unknown parameters are used for cumulative hazard rates. Empirical Bayes estimators are suggested and asymptotic optimality is proved. Our result generalizes that of Susarla and Van Ryzin(1978) in the sensor that (i) the cumulative hazard rate induced by a Dirichlet process is a beta process, (ii) our empirical Bayes estimator does not depend on the censoring distribution while that of Susarla and Van Ryzin(1978) does, (iii) a class of estimators of the hyperprameters is suggested in the prior distribution which is assumed known in advance in Susarla and Van Ryzin(1978). This extension makes the proposed empirical Bayes procedure more applicable to real dta sets.

Keywords

References

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