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Abstract

The paper deals with estimation models using censored life time data. First, a short survey on parametric and nonparametric estimation is given for i.i.d. life times under censorship without repair. Special investigations are made for Koziol-Green models. In the second part, a general failure-repair model described by counting processes is considered. Under the Koziol-Green condition some results concerning Bayes estimation and the nuisance parameter case are obtained.

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References

  1. Abdushukurov, A. A. (1984). On some estimates of the distribution function under random censorship, In Conference of Young Scient Math. Inst. Acad. Sci. Uzbek., Taschkent, No. 8756-V (in Russian).

    Google Scholar 

  2. Breslow, N. E. (1992). Introduction to Kaplan and Meier (1958), Non-parametric estimation from incomplete observations, In Breakthroughs in Statistics, Vol. II (Eds., S. Kotz and N. L. Johnson), pp. 311–318, Methodology and Distribution, New York: Springer-Verlag.

    Google Scholar 

  3. Cheng, P. E. and Lin, G. D. (1984). Maximum likelihood estimation of survival function under the Koziol-Green proportional hazard model, Technical Report B-84–5, Institute of Statistics, Academica Sinica, Taipei, Taiwan

    Google Scholar 

  4. Csörgö, S. (1988). Estimation in the proportional hazards model of random censorship, Statistics, 19, 437–463.

    Article  MathSciNet  Google Scholar 

  5. Ferreira, P. E. (1982). Sequential estimation through estimating equations in the nuisance parameter case, Annals of Statistics, 10, 167–173.

    Article  MathSciNet  MATH  Google Scholar 

  6. Fleming, T. R. and Harrington, D. P. (1991). Counting Processes and Survival Analysis, New York: John Wiley & Sons.

    MATH  Google Scholar 

  7. Franz, J. (1994). On estimation problems in random censored repair models, EQC, 9, 125–142.

    MATH  Google Scholar 

  8. Franz, J. and Magiera, R. (1997a). On information inequalities in sequential estimation for stochastic processes, Mathematical Methods of Oper-atations Research (ZOR), 46, 1–27.

    Article  MathSciNet  MATH  Google Scholar 

  9. Franz, J. and Magiera, R. (1997b). Sequential estimation for a family of counting processes in the nuisance parameter case, Statistical Papers (to appear).

    Google Scholar 

  10. Godambe, V. P. (1960). An optimum property of regular maximum likelihood estimation, Annals of Mathematical Statistics, 31, 1208–1212.

    Article  MathSciNet  Google Scholar 

  11. Godambe, V. P. (1976). Conditional likelihood and unconditional optimum estimating functions, Biometrika, 63, 277–284.

    Article  MathSciNet  MATH  Google Scholar 

  12. Godambe, V. P. (1984). On ancillarity and Fisher information in the presence of a nuisance parameter, Biometrika, 71, 626–629.

    MathSciNet  MATH  Google Scholar 

  13. Godambe, V. P. and Thompson, M. E. (1974). Estimating equations in the presence of a nuisance parameter, Annals of Statistics, 2, 568–574.

    Article  MathSciNet  MATH  Google Scholar 

  14. Hurt, J. (1992). On statistical methods for survival data analysis, Proceedings of the Summer School JČMF (ROBUST 1992), Prague 1992, 54–74.

    Google Scholar 

  15. Kaplan, E. L. and Meier, P. (1958). Nonparametric estimation from incomplete observations, Journal of the American Statistical Association, 53, 457–481.

    Article  MathSciNet  MATH  Google Scholar 

  16. Koziol, J. A. and Green, S. B. (1976). A Cramér-von-Mises statistic for randomly censored data, Biometrika, 63, 456–474.

    MathSciNet  Google Scholar 

  17. Koziol, J. A. (1980). Goodness of fit tests for randomly censored data, Biometrika, 67, 693–696.

    Article  MathSciNet  MATH  Google Scholar 

  18. Liptser, R. S. and Shiryaev, A. N. (1978). Statistics of Random Processes, Vol. II, New York: Springer-Verlag.

    Google Scholar 

  19. Pawlitschko, J. (1996). Die Schätzung einer Überlebensfunktion in Verallgemeinerung des Koziol-Green-Modells, Dissertation, Universität Dortmund.

    Google Scholar 

  20. Pruscha, H. (1985). Parametric inference in Markov branching processes with time-dependent random immigration rate, Journal of Applied Probability, 22, 503–517.

    Article  MathSciNet  MATH  Google Scholar 

  21. Stadje, W. and Zuckerman, D. (1991). Optimal maintenance strategies for repairable systems with general degrees of repair, Journal of Applied Probability, 28, 384–396.

    Article  MathSciNet  MATH  Google Scholar 

  22. Stute, W. and Wang, J.-L. (1993). The strong law under random censorship, Annals of Statistics, 21, 1591–1607.

    Article  MathSciNet  MATH  Google Scholar 

  23. Willing, R. (1987). Semi-sufficiency in accelerated life testing, In Probability and Bayesian Statistics (Ed., R. Viertl), New York: Plenum Press.

    Google Scholar 

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© 1998 Birkhäuser Boston

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Franz, J. (1998). On Statistics in Failure-Repair Models Under Censoring. In: Kahle, W., von Collani, E., Franz, J., Jensen, U. (eds) Advances in Stochastic Models for Reliability, Quality and Safety. Statistics for Industry and Technology. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2234-7_3

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  • DOI: https://doi.org/10.1007/978-1-4612-2234-7_3

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-1-4612-7466-7

  • Online ISBN: 978-1-4612-2234-7

  • eBook Packages: Springer Book Archive

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