Skip to main content
Log in

On probabilities of large deviations for UH-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

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

Instant access to the full article PDF.

References

  1. Yu. V. Borovskikh, Theory ofU-statistics in Hilbert space [in Russian], Preprint 86.78, Inst. of Mathematics, Kiev, 1986, p. 56.

    Google Scholar 

  2. V. S. Korolyuk and Yu. V. Borovskikh, Rate of convergence in the central limit theorem forUH-statistics,Ukrain. Mat. Zh.,42 (8), 1043–1050 (1990).

    MathSciNet  Google Scholar 

  3. T. L. Malevich and B. Abdalimov, Probabilities of large deviations forU-statistics,Theory Probab. Appl.,24 (1), 215–220 (1979).

    Article  MathSciNet  Google Scholar 

  4. M. Vandemaele, On probabilities of large deviations forU-statistics,Theory Probab. Appl.,27 (3), 573–574 (1982).

    MATH  MathSciNet  Google Scholar 

  5. A. K. Aleškevičiené, Probabilities of large deviations forU-statistics and for Mises functionals,Theory Probab. Appl,35 (1), 3–14 (1990).

    MathSciNet  Google Scholar 

  6. A. K. Aleškevičiené, Large deviations forU-statistics,Liet. Mat. Rinkinys,32 (1), 7–19 (1992).

    Google Scholar 

  7. Yu. V. Borovskikh,U-statistics in Banach spaces,Acta Appl. Math.,35 (3), 285–298 (1994).

    Article  MathSciNet  Google Scholar 

  8. A. I. Račkauskas, Probabilities of large deviations in the Linnik zones in Hilbert spaces,Liet. Mat. Rinkinys 28 (3), 520–533 (1988).

    Google Scholar 

  9. W. Hoeffding, A class of statistics with asymptotically normal distribution,Ann. Math. Statist.,19, 293–325 (1948).

    MATH  MathSciNet  Google Scholar 

  10. R. Bentkus and R. Rudzkis, On exponential estimates of the distribution of random variables,Liet. Mat. Rinkinys,20 (1), 15–30 (1980).

    MathSciNet  Google Scholar 

  11. B. A. Zalesskii, Probabilities of large deviations in Hilbert space,Theory Probab. Appl.,34 (4), 650–655 (1989).

    MATH  MathSciNet  Google Scholar 

Download references

Authors

Additional information

Institute of Mathematics and Informatics, Akademijos 4, 2600 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 35, No. 2, pp. 141–151, April–June, 1995.

Translated by A. Aleškevičiené

Rights and permissions

Reprints and permissions

About this article

Cite this article

Aleškevičiené, A., Borovskikh, J. On probabilities of large deviations for UH-statistics. Lith Math J 35, 112–120 (1995). https://doi.org/10.1007/BF02341489

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02341489

Navigation