Skip to main content
SpringerLink
Log in

Bootstrap Approximation of Distributions of the L-Statistics

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

Abstract

We study consistency conditions of the bootstrap approximation for linear combinations of order statistics with coefficients determined by a weight function. Bibliography: 10 titles.

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

Access this article

Log in via an institution

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. K. B. Athreya, “Bootstrap of the mean in the infinite variance case," Ann. Statist., 15, 724-731 (1987).

    Google Scholar 

  2. P. J. Bickel and D. Freedman, “Some asymptotic theory for the bootstrap," Ann. Statist., 9, 1196-1217 (1981).

    Google Scholar 

  3. P. Deheuvels, D. M. Mason, and G. R. Shorack, “Some results on the influence of extremes on the bootstrap," Ann. Inst. Henri Poincaré, 29, 83-103 (1993).

    Google Scholar 

  4. R. Helmers, P. Janssen, and R. Serfling, “Berry-Essen and bootstrap results for generalized L-statistics," Scand. J. Statist., 17, 65-77 (1990).

    Google Scholar 

  5. R. Helmers and H. Putter, “Bootstrap resampling: a survey of recent research in the Netherlands," Amsterdam CWI report, BS-R9519 (1995).

  6. B. Efron and R. J. Tibshirani, Introduction to the Bootstrap, Chapman and Hall, New York (1993).

    Google Scholar 

  7. N. V. Gribkova, “On bootstrap L-statistics," in: “Asymptotic Methods in Probability and Mathematical Statistics," St. Petersburg (1980), pp. 103-106.

  8. K. Singh, “On asymptotic accuracy of Efron's bootstrap," Ann. Statist., 9, 1187-1195 (1981).

    Google Scholar 

  9. S. M. Stigler, “Linear functions of order statistics with smooth weight functions," Ann. Statist., 2, 676-693 (1974).

    Google Scholar 

  10. W. R. van Zwet, “A Berry-Essen bound for symmetric statistic,” Z. Wahrsh. Verv. Gebiete, 66, 425-440 (1984).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. St. Petersburg Railway University, Russia

    N. V. Gribkova

Authors
  1. N. V. Gribkova
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gribkova, N.V. Bootstrap Approximation of Distributions of the L-Statistics. Journal of Mathematical Sciences 109, 2088–2102 (2002). https://doi.org/10.1023/A:1014521131015

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1014521131015

Keywords

Search

Navigation