Skip to main content
SpringerLink
Log in

Nonuniform estimation of rate of convergence for L-statistics

  • Published:
Ukrainian Mathematical Journal Aims and scope

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

Literature cited

  1. W. Rosenkrantz and N. E. O'Reilly, “Application of the Skorohod representation theorem to rates of convergence for Linear combinations of order statistics,” Ann. Math. Statist.,43, No. 4, 1204–1212 (1972).

    Google Scholar 

  2. T. de Wet, “Rates of convergence of linear combinations of order statistics,” South Afr. Statist. G.,8, 35–43 (1974).

    Google Scholar 

  3. S. Bjerve, “Error bounds for linear combinations of order statistics,” Ann. Statist.,5, No. 2, 357–369 (1977).

    Google Scholar 

  4. R. Helmers, “The order of the normal approximation for linear combinations of order statistics with smooth weight functions,” Ann. Probab.,5, No. 6 (1977).

  5. R. Helmers, “A Berry — Esseen theorem for linear combinations of order statistics,” Mathematical Centre Report SW 54/77, Amsterdam (1977).

  6. R. Helmers, “Edgeworth expansion, for linear combinations of order statistics with smooth weight functions,” Mathematical Centre Report SW 44/76, Amsterdam (1976).

  7. W. R. van Zwet, “Asymptotic expansions for the distribution functions of linear combinations of order statistics,” in: Statistical Decision Theory and Related Topics, Vol. 11, Academic Press, New York (1977), pp. 421–438.

    Google Scholar 

  8. S. W. Dharmadhikari and K. Jogdeo, “Bounds on moments of certain random variables with applications, ” Ann. Math. Statist.,40, No. 4, 1506–1508 (1969).

    Google Scholar 

  9. G. D. Esary, F. Proshan, and D. W. Walkup, “Association of random variables with applications,” Ann. Math. Statist.,38, 1466–1474 (1967).

    Google Scholar 

  10. S. M. Stigler, “Linear functions of order statistics with smooth weight functions,” Ann. Statist.,2, No. 4, 676–693 (1974).

    Google Scholar 

  11. Yu. V. Borovskikh, “Approximation of distributions of U-statistics,” Dokl. Akad. Nauk Ukr. SSR, No. 9, 695–698 (1979).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, Academy of Sciences of the Ukrainian SSR, USSR

    Yu. V. Borovskikh

Authors
  1. Yu. V. Borovskikh
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 33, No. 2, pp. 160–166, March–April, 1981.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Borovskikh, Y.V. Nonuniform estimation of rate of convergence for L-statistics. Ukr Math J 33, 127–132 (1981). https://doi.org/10.1007/BF01086067

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01086067

Search

Navigation