Skip to main content
Log in

Asymptotics of the distribution of the ratio of sums of random variables

  • 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.

Literature Cited

  1. C. J. Stone, “Consistent nonparametric regression,” Ann. Statist.,5, No. 4, 595–620 (1977).

    Google Scholar 

  2. Y. Stoyanov, “Probabilistic proof of the convergence of the class of n-fold integrals,” Glas. Math. Ser. III,21, No. 1, 101–114 (1986).

    Google Scholar 

  3. J. V. Uspensky, “Problems and solutions,” Amer. Math. Monthly,39, No. 1, 176–177 (1932).

    Google Scholar 

  4. B. F. Kimball, “Problems and solutions,” Amer. Math. Monthly,37, 508 (1930).

    Google Scholar 

  5. Ya. Galambos, The Asymptotic Theory of Extremal Order Statistics [in Russian], Nauka, Moscow (1984).

    Google Scholar 

  6. S. Csörgö, P. Deheuvels, and D. M. Mason, “Kernel estimates of the tail index of a distribution,” Ann. Stat.,13, No. 2, 1050–1077 (1985).

    Google Scholar 

  7. E. Haeusler and J. L. Teugels, “On asymptotic normality of Hill's estimator for the exponent of regular variation,” Ann. Stat.,13, No. 2, 743–756 (1985).

    Google Scholar 

  8. B. M. Hill, “A simple approach to inference about the tail of a distribution,” Ann. Stat.,3, 1163–1174 (1975).

    Google Scholar 

  9. K. Noda, “Estimation of a regression function by Parzen kernel-type density estimators,” Ann. Inst. Stat. Math.,28, No. 2, 221–234 (1976).

    Google Scholar 

  10. G. Collomb, “Quelques propriétés de la méthode du noyau pour l'estimation non paramétrique de la régression en un point fixé,” C. R. Acad. Sci. Paris,285A, No. 4, 289–292 (1977).

    Google Scholar 

  11. M. Loève, Probability Theory, Van Nostrand, Princeton (1960).

    Google Scholar 

  12. A. A. Borovkov, Probability Theory [in Russian], Nauka, Moscow (1986).

    Google Scholar 

  13. M. Csörgö, L. Horváth, and P. Révész, “On the optimality of estimating the tail index and a naive estimator,” Aust. J. Stat.,29, No. 2, 166–178 (1987).

    Google Scholar 

Download references

Authors

Additional information

Novosibirsk. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 31, No. 5, pp. 92–101, September–October, 1990.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Novak, S.Y., Utev, S.A. Asymptotics of the distribution of the ratio of sums of random variables. Sib Math J 31, 781–788 (1990). https://doi.org/10.1007/BF00974491

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00974491

Navigation