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Uniform Consistency for Conditional Lifetime Distribution Estimators Under Random Right-Censorship

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Advances in Statistical Methods for the Health Sciences

Part of the book series: Statistics for Industry and Technology ((SIT))

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Abstract

We define nonparametric kernel-type estimators of the conditional distribution of a lifetime, in a random censorship framework. We show that these estimators have closed-form expressions, and establish their strong uniform consistency under minimal assumptions.

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References

  1. Burke, M. D., Csörgő, S., and Horváth, L. (1981). Strong approximations of some biometric estimates under random censorship, Z. Wahrsch. Verw. Gebiete, 56, 87–112.

    Article  MATH  MathSciNet  Google Scholar 

  2. Burke, M. D., Csörgő, S., and Horváth, L. (1988). A correction to and an improvement of strong approximations of some biometric estimates under random censorship, Probability Theory and Related Fields, 56, 87–112.

    Google Scholar 

  3. Deheuvels, P., and Einmahl, J. H. J. (2000). Functional limit laws for the increments of Kaplan-Meier product-limit processes and applications, The Annals of Statistics, 28, 1301–1335.

    MATH  MathSciNet  Google Scholar 

  4. Deheuvels, P., and Mason, D. M. (2004). General asymptotic confidence bands based on kernel-type function estimators, Statistical Inference for Stochastic Processes, 7, 225–277.

    Article  MATH  MathSciNet  Google Scholar 

  5. Einmahl, U., and Mason, D. M. (2000). An empirical approach to the uniform consistency of kernel-type function estimators, Journal of Theoretical Probability, 13, 1–37.

    Article  MATH  MathSciNet  Google Scholar 

  6. Einmahl, U., and Mason, D. M. (2005). Uniform in bandwidth consistency of kernel-type function estimators, Annals of Probability, 33, 1380–1403.

    Article  MATH  MathSciNet  Google Scholar 

  7. Földes, A., Rejtő, L., and Winter, B. B. (1981). A LIL type result for the product-limit estimator, Z. Wahrsch. Verw. Gebiete, 56, 75–86.

    Article  MATH  MathSciNet  Google Scholar 

  8. Gill, R. D. (1980). Censoring and Stochastic Integrals, Mathematisch Centrum Tracts, Amsterdam, The Netherlands.

    MATH  Google Scholar 

  9. Härdle, W. (1990). Applied Nonparametric Regression, Cambridge University Press, Cambridge.

    MATH  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  11. Nadaraya, E. A. (1964). On estimating regression, Theory of Probability and Its Applications, 9, 141–142.

    Article  Google Scholar 

  12. Nadaraya, E. A. (1989). Nonparametric Estimation of Probability Densities and Regression Curves, Kluwer, Dordrecht, The Netherlands.

    MATH  Google Scholar 

  13. Watson, G. S. (1964). Smooth regression analysis, Sankhyā, Series A, 26, 359–372.

    MATH  Google Scholar 

  14. Stute, W. (1986). On almost sure convergence of conditional empirical distribution functions, The Annals of Statistics, 14, 891–901.

    MATH  Google Scholar 

  15. Stute, W. (1995). The central limit theorem under random censorship, The Annals of Statistics, 23, 86–107.

    MathSciNet  Google Scholar 

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© 2007 Birkhäuser Boston

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Deheuvels, P., Derzko, G. (2007). Uniform Consistency for Conditional Lifetime Distribution Estimators Under Random Right-Censorship. In: Auget, JL., Balakrishnan, N., Mesbah, M., Molenberghs, G. (eds) Advances in Statistical Methods for the Health Sciences. Statistics for Industry and Technology. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4542-7_13

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