Skip to main content
SpringerLink
Log in

Approximation of distributions of von Mises statistics with multidimensional kernels

  • 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

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. Yu. V. Borovskikh and V. S. Korolyuk, The Theory of U-Statistics [in Russian], Naukova Dumka, Kiev (1989).

    Google Scholar 

  2. H. Dehling, M. Denker, and W. Philipp, “A bounded law of the iterated logarithm for Hilbert space valued martingales and its application to U-statistics,” Probab. Theor. Rel. Fields,72, No. 1, 111–131 (1986).

    Google Scholar 

  3. D. Nolan and D. Pollard, “Functional limit theorems for U-processes,” Ann. Probab.,16, No. 3, 1291–1298 (1988).

    Google Scholar 

  4. V. V. Yurinskii, “Exponential inequalities for sums of random variables,” J. Multiv. Anal.,6, No. 4, 473–499 (1976).

    Google Scholar 

  5. A. A. Filippova, “Von Mises' theorem on the asymptotic behavior of functionals of empirical distribution functions and its statistical applications,” Teor. Veroyatn. Primen.,7, No. 2, 26–60 (1962).

    Google Scholar 

  6. P. Major, Multiple Wiener-Ito Integrals, Lecture Notes in Mathematics, Vol. 849, Springer-Verlag, Berlin (1981).

    Google Scholar 

  7. W. A. Woyczynski, “Geometry and martingales in Banach spaces. Ia,” in: Lecture Notes in Mathematics, Vol. 472, Springer-Verlag, Berlin (1975), pp. 229–275.

    Google Scholar 

  8. W. A. Woyczynski, “Geometry and martingales in Banach spaces. II,” in: Adv. Probab., Vol. 4, Marcel Dekker, New York (1978), pp. 267–318.

    Google Scholar 

  9. P. Major, “On the tail behavior of the distribution function of multiple stochastic integrals,” Probab. Theor. Rel. Fields,78, No. 3, 419–438 (1988).

    Google Scholar 

  10. I. S. Borisov, “On the problem of accuracy of approximations in the central limit theorem for empirical measures,” Sib. Mat. Zh.,24, No. 6, 14–25 (1983).

    Google Scholar 

  11. I. S. Borisov, “On the rate of convergence in the ‘conditional’ invariance principle,” Teor. Veroyatn. Primen.,23, No. 1, 67–69 (1978).

    Google Scholar 

  12. V. M. Zolotarev, “One-sided interpretation and refinement of some inequalities of the Chebyshev type,” Lit. Mat. Sb.,5, No. 2, 233–250 (1965).

    Google Scholar 

  13. A. Araujo and E. Gine, The Central Limit Theorem for Real and Banach Valued Random Variables, Wiley, New York (1980).

    Google Scholar 

Download references

Authors
  1. I. S. Borisov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Novosibirsk. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 32, No. 4, pp. 20–35, July–August, 1991.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Borisov, I.S. Approximation of distributions of von Mises statistics with multidimensional kernels. Sib Math J 32, 554–566 (1991). https://doi.org/10.1007/BF00972974

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00972974

Keywords

Search

Navigation