Skip to main content
SpringerLink
Log in

Probabilities of large deviations for L-statistics

  • Published:
Lithuanian Mathematical Journal Aims and scope Submit manuscript

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. I. A. Ibragimov and Yu. V. Linnik, Independent and Stationarily Correlated Variables [in Russian], Nauka Moscow (1965).

    Google Scholar 

  2. V. V. Petrov, Sums of Independent Random Variables [in Russian], Nauka, Moscow (1972).

    Google Scholar 

  3. L. Saulis and V. Statulevicius, Limit Theorems for Large Deviations [in Russian], Mokslas, Vilnius (1989).

    Google Scholar 

  4. P. Groeneboom and G. R. Shorack, “Large deviations of fit statistics and linear combinations of order statistics,” Ann. Prob.,9, No. 6, 971–987 (1981).

    Google Scholar 

  5. M. Vandemaele and N. Veraverbeke, “Cramer-type large deviations for linear combinations of order statistics,” Ann. Prob.,10, No. 2, 423–434 (1982).

    Google Scholar 

  6. M. L. Puri and M. Seoh, “On the rate of convergence in normal approximation and large deviations probabilities for a class of statistics,” Theor. Prob. Appl.,33, No. 4, 735–750 (1988).

    Google Scholar 

  7. A. Aleskeviciene, “On large deviations for linear combinations of order statistics,” Liet. Mat. Rinkinys,29, No. 2, 212–222 (1989).

    Google Scholar 

  8. V. Bentkus, “On large deviations in Banach spaces,” Theor. Prob. Appl.,31, No. 4, 710–716 (1986).

    Google Scholar 

  9. V. Bentkus and A. Rackauskas, “On probabilities of large deviations in Banach spaces,” (to be published in Probab. Theor. and Rel. Fields).

  10. Z. Govindarajulu and D. M. Mason, “A strong representation for linear combinations of order statistics with application to fixed-width confidence intervals for location and scale parameters,” Scand. J. Statist.,10, No. 2, 97–115 (1983).

    Google Scholar 

  11. H.-H. Kuo, “Gaussian measures in Banach spaces,” Lec. Notes Math.,463, Springer Verlag, Berlin (1975).

    Google Scholar 

  12. R. Rudzkis, L. Saulis, and V. A. Statulevicius, “A general lemma on probabilities of large deviations,” Liet. Mat. Rinkinys,28, No. 2, 99–116 (1988).

    Google Scholar 

  13. R. Bentkus and R. Rudzkis, “On exponential estimates of the distribution of random variables,” Liet. Mat. Rinkinys, No. 1, 15–30 (1980).

    Google Scholar 

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

    Google Scholar 

  15. R. J. Serfling, Approximation Theorems of Mathematical Statistics, Wiley, New York (1980).

    Google Scholar 

  16. R. Helmers, Edgeworth Expansions for Linear Combinations of Order Statistics, Mathematical centre tracts, No. 105, Amsterdam (1982).

  17. G. R. Shorack, “Functions of order statistics,” Ann. Math. Statist.,43, 412–427 (1972).

    Google Scholar 

Download references

Authors
  1. V. Bentkus
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. Zitikis
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Institute of Mathematics and Cybernetics, Academy of Sciences of the Lithuanian SSR, Vilnius University. Translated from Litovskii Matematicheskii Sbornik (Lietuvos Matematikos Rinkinys), Vol. 30, No. 3, pp. 479–488, July–September, 1990.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bentkus, V., Zitikis, R. Probabilities of large deviations for L-statistics. Lith Math J 30, 215–222 (1990). https://doi.org/10.1007/BF00970804

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00970804

Search

Navigation