Skip to main content
Log in

Probability Inequalities for Generalized L-Statistics

  • Published:
Siberian 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

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

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Zitikis R., “Smoothness of the distribution function of an ℳℒ-statistic. I,” Lithuanian Math. J., 30, No. 2, 97-106 (1990).

    Google Scholar 

  2. Zitikis R., “Smoothness of the distribution function of an ℳ ℒ-statistic. II,” Lithuanian Math. J., 30, No. 3, 231-240 (1990).

    Google Scholar 

  3. Borisov I. S., “Bounds for characteristic functions of additive functionals of order statistics,” Siberian Adv. Math., 5, No. 4, 1-15 (1995).

    Google Scholar 

  4. Aleshkyavichene A. K., “On large deviations for linear combinations of order statistics,” Litovsk. Mat. Sb., 29, No. 2, 212-222 (1989).

    Google Scholar 

  5. Borisov I. S. and Baklanov E. A., “Moment inequalities for generalized L-statistics,” Siberian Math. J., 39, No. 3, 415-421 (1998).

    Google Scholar 

  6. Serfling R. J., “Generalized L-, M-, and R-statistics,” Ann. Probab., 12, No. 1, 76-86 (1984).

    Google Scholar 

  7. Borisov I. S., “On the rate of convergence in the ‘conditional’ invariance principle,” Theory Probab. Appl., 23, No. 1, 63-76 (1978).

    Google Scholar 

  8. Pinelis I. F. and Sakhanenko A. I., “Remarks on inequalities for large deviation probabilities,” Theory Probab. Appl., 30, No. 1, 143-148 (1985).

    Google Scholar 

  9. Nagaev S. V. and Pinelis I. F., “Some inequalities for the distributions of sums of independent random variables,” Theory Probab. Appl., 22, 248-256 (1977).

    Google Scholar 

  10. Chernoff H., Gastwirth J. L., and Johns M. V. Jr., “Asymptotic distribution of linear combinations of order statistics, with applications to estimation,” Ann. Math. Statist., 38, 52-72 (1967).

    Google Scholar 

  11. Helmers R., “A Berry-Esseen theorem for linear combinations of order statistics,” Ann. Probab., 9, No. 2, 342-347 (1981).

    Google Scholar 

  12. Mason D. M. and Shorack G. R., “Necessary and sufficient conditions for asymptotic normality of L-statistics,” Ann. Probab., 20, No. 4, 1779-1804 (1992).

    Google Scholar 

  13. Norvaiša R. and Zitikis R., “Asymptotic behaviour of linear combinations of functions of order statistics,” J. Statist. Planning and Inference, 28, 305-317 (1991).

    Google Scholar 

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

    Google Scholar 

  15. Aleshkyavichene A. K., “Large and moderate deviations for L-statistics,” Lithuanian Math. J., 31, No. 2, 145-156 (1991).

    Google Scholar 

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

    Google Scholar 

  17. Feller W., An Introduction to Probability Theory and Its Applications. Vol. 2, Wiley, New York (1970).

    Google Scholar 

  18. Feller W., An Introduction to Probability Theory and Its Applications. Vol. 1, Wiley, New York (1971).

    Google Scholar 

  19. Pinelis I. F., “Estimates for moments of infinite-dimensional martingales,” Math. Notes, 27, No. 6, 459-462 (1980).

    Google Scholar 

  20. Nagaev S. V. “Probability inequalities for sums of independent random variables with values in a Banach space,” in: Advances in Probability Theory: Limit Theorems and Related Problems (A. A. Borovkov, ed.), Optimization Software, Inc., New York, 1982, pp.293-307.

    Google Scholar 

  21. Pinelis I. F., “Inequalities for distributions of sums of independent random vectors and their application to estimating a density,” Theory Probab. Appl., 35, No. 3, 605-607 (1990).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Borisov, I.S., Baklanov, E.A. Probability Inequalities for Generalized L-Statistics. Siberian Mathematical Journal 42, 217–231 (2001). https://doi.org/10.1023/A:1004828827948

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1004828827948

Keywords

Navigation