Skip to main content
SpringerLink
Log in

Estimate of the bounded lipschitz metric for sums of weakly dependent random variables

  • 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

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. S. N. Bernshtein, Collected Works [in Russian], Vol. IV, Nauka, Moscow (1964).

    Google Scholar 

  2. V. A. Volkonskii and Yu. A. Rozanov, “Limit theorems for random functions. I,” Teor. Veroyatn. Primen.,4, No. 2, 186–207 (1959).

    Google Scholar 

  3. Yu. A. Davydov, “Convergence of distributions generated by stationary stochastic processes,” Teor. Veroyatn. Primen.,13, No. 4, 730–737 (1968).

    Google Scholar 

  4. I. A. Ibragimov, “Limit theorems for stationary processes,” Teor. Veroyatn. Primen.,7, No. 4, 361–392 (1962).

    Google Scholar 

  5. I. Sunklodas, “Distance in the metric of L1 of the distribution of the sum of weakly dependent random variables from a normal distribution function,” Liet. Mat. Rinkinys,22, No. 2, 171–188 (1982).

    Google Scholar 

  6. I. Sunklodas, “Approximation of distributions of sums of weakly dependent random variables by a normal distribution,” Liet. Mat. Rinkinys,27, No. 4, 766–778 (1987).

    Google Scholar 

  7. A. D. Barbour and G. K. Eagleson, “Multiple comparisons and sums of dissociated random variables,” Adv. Appl. Prob.,17, 147–162 (1985).

    Google Scholar 

  8. J. R. Blum, D. L. Hanson, and L. H. Koopmans, “On the strong law of large numbers for a class of stochastic processes,” Z. Wahr. Verw. Geb.,2, No. 1, 1–11 (1963).

    Google Scholar 

  9. C. Chipp, “Convergence rates of the strong law for stationary mixing sequences,” Z. Wahr. Verw. Geb.,49, No. 1, 49–62 (1979).

    Google Scholar 

  10. R. V. Erickson, “L1 bounds for asymptotic normality of m-dependent sums using Stein's techniques,” The Ann. Prob.,2, No. 3, 522–529 (1974).

    Google Scholar 

  11. W. Hoeffding and H. Robbins, “The central limit theorem for dependent random variables,” Duke Math. J.,15, 773–780 (1948).

    Google Scholar 

  12. W. Philipp, “The central limit problem for mixing sequences of random variables,” Z. Wahr. Verw. Geb.,12, No. 2, 155–171 (1969).

    Google Scholar 

  13. V. A. Statulevicius, “Application of semiinvariants to asymptotic analysis of distributions of random processes,” Multivariate Analysis,4, 325–327 (1977).

    Google Scholar 

  14. C. Stein, “A bound for the error in the normal approximation to the distribution of a sum of dependence random variables,” in: Proc. 6th Berkeley Symp. Math. Statist. Prob., Vol. 2, Univ. California Press (1972), pp. 583–602.

  15. H. Takahata, “L∞-bound for asymptotic normality of weakly dependent summands using stein's results,” The Ann. Prob.,9, No. 4, 676–683 (1981).

    Google Scholar 

Download references

Authors
  1. J. Sunklodas
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Institute of Mathematics and Cybernetics, Academy of Sciences of the Lithuanian SSR. Translated from Litovskii Matematicheskii Sbornik (Lietuvos Matematikos Rinkinys), Vol. 29, No. 2, pp. 385–393, April–June, 1989.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sunklodas, J. Estimate of the bounded lipschitz metric for sums of weakly dependent random variables. Lith Math J 29, 187–193 (1989). https://doi.org/10.1007/BF00966080

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00966080

Keywords

Search

Navigation