Skip to main content
Log in

Martingale estimates for the distribution of the deviation of density estimates

  • Brief Communications
  • 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

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

Instant access to the full article PDF.

Literature cited

  1. V. S. Korolyuk and Yu. V. Borovskikh, The Martingale Theory of U-Statistics [in Russian], Preprint, Akad. Nauk Ukr. SSR, Inst. Mat., 84.63, Kiev (1984), p. 56.

    Google Scholar 

  2. V. S. Korolyuk and Yu. V. Borovskikh, Asymptotic Analysis of Distributions of Statistics [in Russian], Naukova Dumka, Kiev (1984).

    Google Scholar 

  3. Yu. V. Borovskikh, The Problem of Approximating Distributions of U-Statistics and Mises Functionals, II [in Russian], Preprint, Akad. Nauk Ukr. SSR, Inst. Mat., 80.7, Kiev (1980).

    Google Scholar 

  4. E. A. Nadaraya, “The application of the central limit theorem for Martingales to the study of the limiting distribution of the square deviation of the estimate of the density of a type of kernel,” Soobshch. Akad. Nauk TSSR,113, No. 2, 253–256 (1984).

    Google Scholar 

  5. R. Sh. Liptser and A. N. Shiryaev, “The functional central limit theorem for semi martingales,” Teor. Veroyatn. Primen.,25, No. 4, 683–703 (1980).

    Google Scholar 

  6. P. Hall, “Central limit theorem for integrated square error of multivariate nonparamettric density estimators,” J. Multivar. Anal.,14, No. 1, 1–16 (1984).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 38, No. 1, pp. 105–107, January–February, 1986.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Korolyuk, V.S., Melyaeva, O. Martingale estimates for the distribution of the deviation of density estimates. Ukr Math J 38, 94–97 (1986). https://doi.org/10.1007/BF01056768

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01056768

Keywords

Navigation