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A correction to and improvement of ‘Strong approximations of some biometric estimates under random censorship’
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  • Published: September 1988

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

  • Murray D. Burke1,
  • Sándor Csörgő2 &
  • Lajos Horváth3 

Probability Theory and Related Fields volume 79, pages 51–57 (1988)Cite this article

  • 107 Accesses

  • 44 Citations

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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.

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References

  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)

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  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)

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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Calgary, T2N 1N4, Calgary, Alberta, Canada

    Murray D. Burke

  2. Bolyai Institute, Szeged University, Aradi vértanúk tere 1, H-6720, Szeged, Hungary

    Sándor Csörgő

  3. Department of Statistics, University of Wisconsin-Madison, 53705, Madison, WI, USA

    Lajos Horváth

Authors
  1. Murray D. Burke
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  2. Sándor Csörgő
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  3. Lajos Horváth
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Burke, M.D., Csörgő, S. & Horváth, L. A correction to and improvement of ‘Strong approximations of some biometric estimates under random censorship’. Probab. Th. Rel. Fields 79, 51–57 (1988). https://doi.org/10.1007/BF00319103

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  • Received: 03 March 1986

  • Revised: 01 February 1988

  • Issue Date: September 1988

  • DOI: https://doi.org/10.1007/BF00319103

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Keywords

  • Stochastic Process
  • Probability Theory
  • Statistical Theory
  • Gaussian Process
  • Empirical Process
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