Advertisement

Kiefer's theorem via the Hungarian construction

  • Galen R. Shorack
Article

Summary

A proof of Kiefer's theorem estimating the difference between the empirical and quantile processes is given by appealing to the Hungarian construction.

Keywords

Stochastic Process Probability Theory Mathematical Biology Quantile 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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bahadur, R.: A note on quantiles in large samples. Ann. Math. Statist. 37, 577–580 (1966)Google Scholar
  2. 2.
    Csörgö, M., Révész, P.: Strong Approximations in Probability and Statistics. New York: Academic Press 1981Google Scholar
  3. 3.
    Kiefer, J.: Deviations between the sample quantile process and the sample D.F. Nonparametric Techniques in Statistícal Inference (M. Puri, Ed.) 299–319. London: Cambridge Univ. Press 1970Google Scholar
  4. 4.
    Mason, D., Shorack, G., Wellner, J.: Strong limit theorems for oscillation moduli of the uniform empirical process. Unpublished technical report (1982)Google Scholar
  5. 5.
    Stute, W.: The oscillation behavior of empirical processes. Ann. Probab. 10, 86–107 (1982)Google Scholar

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • Galen R. Shorack
    • 1
  1. 1.Department of StatisticsUniv. of WashingtonSeattleUSA

Personalised recommendations