Skip to main content

Advertisement

SpringerLink
Log in
Menu
Find a journal Publish with us
Search
Cart
  1. Home
  2. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
  3. Article
Strong approximations of some biometric estimates under random censorship
Download PDF
Download PDF
  • Published: March 1981

Strong approximations of some biometric estimates under random censorship

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

Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete volume 56, pages 87–112 (1981)Cite this article

  • 163 Accesses

  • 80 Citations

  • Metrics details

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

References

  1. Anderson, T.W.: A modification of the sequential probability ratio test to reduce the sample size. Ann. Math. Statist. 31, 165–197 (1960)

    Google Scholar 

  2. Berman, S.M.: A note on extreme values, competing risks and semi-Markov processes. Ann. Math. Statist. 34, 1104–1106 (1963)

    Google Scholar 

  3. Breslow, N., Crowley, J.: A large sample study of the life table and product limit estimates under random censorship. Ann. Statist. 2, 437–453 (1974)

    Google Scholar 

  4. Csörgő, M., Révész, P.: Strong approximations in probability and statistics. New York: Academic Press 1981

    Google Scholar 

  5. Csörgő, S.: Limit behaviour of the empirical characteristic function. Ann. Probability 9, (1981)

  6. Csörgő, S., Horváth, L.: On the Koziol-Green model of random censorship. Biometrika 68 (1981). To appear

  7. Dvoretzky, A., Kiefer, J., Wolfowitz, J.: Asymptotic minimax character of the sample distribution function and of the multinomial estimator. Ann. Math. Statist. 27, 642–669 (1956)

    Google Scholar 

  8. Efron, B.: The two-sample problem with censored data. Proc. Fifth Berkeley Symp. Math. Statist. Probability 4, 831–853 (1967)

    Google Scholar 

  9. Földes, A., Rejtő, L.: Strong uniform consistency for non-parametric survival estimators from randomly censored data. Preprint

  10. Földes, A., Rejtő, L.: Asymptotic properties of the non-parametric survival curve estimators under variable censoring. Preprint

  11. Földes, A., Rejtő, L.: A LIL type result for the product limit estimator on the whole line. Preprint

  12. Földes, A., Rejtő, L., Winter, B.B.: Strong consistency properties of nonparametric estimators for randomly censored data. In: Trans. Eighth Prague Conference Information Theory etc. Vol. C, 105–121. Prague: Academia 1979

    Google Scholar 

  13. Földes, A., Rejtő, L., Winter, B.B.: Strong consistency properties of nonparametric estimators for randomly censored data. Periodica Math. Hung. 11, 233–250 (1980)

    Google Scholar 

  14. Gillespie, M.J., Fisher, L.: Confidence bands for the Kaplan-Meier survival curve estimate. Ann. Statist. 7, 920–924 (1979)

    Google Scholar 

  15. Horváth, L.: Two-problems under random censorship. To appear in: Colloquia Math. Soc. Janos Bolyai. Nonparametric Statistical Inference. Budapest, 1980. I. Vincze, Ed., North-Holland

    Google Scholar 

  16. Kaplan, E.L., Meier, P.: Nonparametric estimation from incomplete observations. J. Amer. Statist. Assoc. 53, 457–481 (1958)

    Google Scholar 

  17. Komlós, J., Major, P., Tusnády, G.: An approximation of partial sums of independent r.v.'s and the sample d.f. I. Z. Wahrscheinlichkeitstheorie verw. Gebiete 32, 111–132 (1975)

    Google Scholar 

  18. Koziol, J.A., Green, S.B.: A Cramér-von Mises statistic for randomly censored data. Biometrika 63, 465–474 (1976)

    Google Scholar 

  19. Meier, P.: Estimation of a distribution function from incomplete observations. In: Perspectives in Probability and Statistics. J. Gani, ed. 67–87. New York: Academic Press 1975

    Google Scholar 

  20. Tsiatis, A.: A nonidentifiability aspect of the problem of competing risks. Proc. Nat. Acad. Sci. U.S.A. 72, 20–22 (1975)

    Google Scholar 

  21. Tusnády, G.: Investigations of statistical hypotheses (in Hungarian). Candidatus dissertation. Hungarian Academy of Sciences (1978)

  22. Winter, B.B., Földes, A., Rejtő, L.: Glivenko-Cantelli theorems for the product limit estimate. Problems of Control and Information Theory 7, 213–225 (1978)

    Google Scholar 

  23. Yang, G.L.: Estimation of a biometric function. Ann. Statist. 6, 112–116 (1978)

    Google Scholar 

  24. Yang, G.: Life expectancy under random censorship. Stochastic Processes Appl. 6, 33–39 (1977)

    Google Scholar 

Download references

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, H-6720, Aradi vertanuk tere 1, Hungary

    Sándor Csörgő

  3. Bolyai Institute, Szeged University, H-6720, Aradi vertanuk tere 1, Hungary

    Lajos Horváth

Authors
  1. Murray D. Burke
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sándor Csörgő
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Lajos Horváth
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Partially supported by a Canadian NSERC grant

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Burke, M.D., Csörgő, S. & Horváth, L. Strong approximations of some biometric estimates under random censorship. Z. Wahrscheinlichkeitstheorie verw. Gebiete 56, 87–112 (1981). https://doi.org/10.1007/BF00531976

Download citation

  • Received: 15 May 1980

  • Issue Date: March 1981

  • DOI: https://doi.org/10.1007/BF00531976

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Keywords

  • Stochastic Process
  • Probability Theory
  • Mathematical Biology
  • Strong Approximation
  • Random Censorship
Download PDF

Working on a manuscript?

Avoid the common mistakes

Advertisement

Search

Navigation

  • Find a journal
  • Publish with us

Discover content

  • Journals A-Z
  • Books A-Z

Publish with us

  • Publish your research
  • Open access publishing

Products and services

  • Our products
  • Librarians
  • Societies
  • Partners and advertisers

Our imprints

  • Springer
  • Nature Portfolio
  • BMC
  • Palgrave Macmillan
  • Apress
  • Your US state privacy rights
  • Accessibility statement
  • Terms and conditions
  • Privacy policy
  • Help and support

167.114.118.210

Not affiliated

Springer Nature

© 2023 Springer Nature