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Probability Theory and Related Fields

, Volume 79, Issue 1, pp 51–57 | Cite as

A correction to and improvement of ‘Strong approximations of some biometric estimates under random censorship’

  • Murray D. Burke
  • Sándor Csörgő
  • Lajos Horváth
Article

Summary

In the proof of the main result of the original paper there is an error. Instead of repairing that proof to get just the original result, at the critical spot we improve the proof and obtain a much better result. In particular, we approximate the product-limit and empirical cumulative hazard processes by suitable copies of the corresponding limiting Gaussian processes with rates of approximation that on appropriate fixed half lines reduce to the rates of Komlós, Major and Tusnády for the uncensored empirical process.

Keywords

Stochastic Process Probability Theory Statistical Theory Gaussian Process Empirical Process 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Burke, M.D., Csörgő, S., Horváth, L.: Strong approximations of some biometric estimates under random censorship. Z. Wahrscheinlichkeitstheor. Verw. Geb. 56, 87–112 (1981)Google Scholar
  2. 2.
    Dehling, H., Denker, M., Philipp, W.: The almost sure invariance principle for the empirical process of U-statistic structure. Ann. Inst. Henri Poincaré 23, 121–134 (1987)Google Scholar

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • Murray D. Burke
    • 1
  • Sándor Csörgő
    • 2
  • Lajos Horváth
    • 3
  1. 1.Department of Mathematics and StatisticsUniversity of CalgaryCalgaryCanada
  2. 2.Bolyai InstituteSzeged UniversitySzegedHungary
  3. 3.Department of StatisticsUniversity of Wisconsin-MadisonMadisonUSA

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