Skip to main content
Log in

On Bahadur's representation of sample quantiles

  • Published:
Annals of the Institute of Statistical Mathematics Aims and scope Submit manuscript

Abstract

We extend the well known transformation technique for order statistics to get less restrictive conditions for the Bahadur representation of sample quantiles.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Ash, J. M., Erdös, P. and Rubel, L. A. (1974). Very slowly varying functions,Aeq. Math.,10, 1–9.

    Article  MathSciNet  Google Scholar 

  2. Bahadur, R. R. (1966). A note on quantiles in large samplcs,Ann. Math. Statist.,37, 577–580.

    Article  MathSciNet  Google Scholar 

  3. Csörgö, M. and Révész, P. (1978). Strong approximations of the quantile process,Ann. Statist.,6, 882–894.

    Article  MathSciNet  Google Scholar 

  4. Ghosh, J. K. (1971). A new proof of Bahadur's representation of quantiles and an application,Ann. Math. Statist.,42, 1957–1961.

    Article  MathSciNet  Google Scholar 

  5. Ghosh, M. and Sukathme, S. (1974). Bahadur representation of quantiles in nonregular cases, Technical Report Statistical Laboratory Iowa State University.

  6. de Haan, L. (1974). On sample quantiles from a regularly varying distribution function,Ann. Statist.,2, 815–818.

    Article  MathSciNet  Google Scholar 

  7. Hoeffding, W. (1963). Probability inequalities for sums of bounded random variables,J. Amer. Statist. Ass.,58, 13–30.

    Article  MathSciNet  Google Scholar 

  8. Kiefer, J. (1967). On Bahadur's representation of sample quantiles,Ann. Math. Statist.,38, 1323–1342.

    Article  MathSciNet  Google Scholar 

  9. Sen, P. K. (1968). Asymptotic normality of sample quantiles form-dependent processes,Ann. Math. Statist.,39, 1724–1730.

    Article  MathSciNet  Google Scholar 

  10. Smirnov, N. V. (1949). Limit distributions for the terms of a variational series,Amer. Math. Soc. Transl. Ser., (1)11, 82–143.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

About this article

Cite this article

de Haan, L., Taconis-Haantjes, E. On Bahadur's representation of sample quantiles. Ann Inst Stat Math 31, 299–308 (1979). https://doi.org/10.1007/BF02480286

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02480286

Keywords

Navigation