Skip to main content
SpringerLink
Log in

Moment inequalities and weak convergence for negatively associated sequences

  • Published:
Science in China Series A: Mathematics Aims and scope Submit manuscript

Abstract

A probability inequality for Sn and somepth moment (p⩾2) inequalities for |Sn| and max 1⩽k⩽n | Sk| are established. Here Sn is the partial sum of a negatively associated sequence. Based on these inequalities, a weak invariance principle for strictly stationary negatively associated sequences is proved under some general conditions.

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.

Similar content being viewed by others

References

  1. Esary, J., Proschan, F., Walkup, D., Association of random variables with applications,Ann. Math. Statist., 1967, 38: 1466.

    Article  MATH  MathSciNet  Google Scholar 

  2. Lehmann, E.L., Some concepts of dependence,Ann. Math. Statist., 1966, 37: 1137.

    Article  MATH  MathSciNet  Google Scholar 

  3. Joag-Dev, K., Proschan, F., Negative association of random variables with applications,Ann. Statist., 1983, 11: 286.

    Article  MathSciNet  Google Scholar 

  4. Block, H.W., Savits, T.H., Shaked, M., Some concepts of negative dependence,Ann. Probab., 1982, 10: 765.

    Article  MATH  MathSciNet  Google Scholar 

  5. Newman, C. L.. Asymptotic independence and limit theorems for positively and negatively dependent random variables, inlnequalities in Statistics and Probability (ed. Tong, Y.L.),IMS Lecture Notes-Monograph Series, Vol.5, 1984, 127–140.

  6. Matula, P., A note on the almost sure convergence of sums of negatively dependent random variables,Statist. Probab. Lett., 1992. 15: 209.

    Article  MATH  MathSciNet  Google Scholar 

  7. Petrov, V.V.,Limit Theorems of Sums of Independent Random Variables (inRussian). Moscow: Nauka, 1987.

    Google Scholar 

  8. Su Chun, A theorem of Hsu-Robbins type for negatively associated sequence,Chinese Science.Bulletin, 1996, 41(6): 441.

    MATH  MathSciNet  Google Scholar 

  9. Newman, C.M., Wright, A.L.. An invariance principle for ertain dependent sequences,Ann. Probab., 1981, 9: 671.

    Article  MATH  MathSciNet  Google Scholar 

  10. Nagaev, S.V., Large deviation of sums of independent random variables,Ann. Probub., 1979, 7: 745.

    Article  MATH  MathSciNet  Google Scholar 

  11. Stout, W.,Almost Sure Convergence, New York: Academic Press. 1974, 204–209.

    MATH  Google Scholar 

  12. Billingsley, P.,Convergence of Probability Measures, New York: John Wiley, 1968.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistics and Finance, University of Science and Technology of China, 230026, Hefei, China

    Chun Su & Lincheng Zhao

  2. Department of Mathematics, Zhanjiang Normal Institute, 524048, Zhanjiang, China

    Yuebao Wang

Authors
  1. Chun Su
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lincheng Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yuebao Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Project supported by the National Natural Science Foundation of China, the Doctoral Program Foundation of the State Education Commission of China and the High Eductional Natural Science Foundation of Guangdong Province.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Su, C., Zhao, L. & Wang, Y. Moment inequalities and weak convergence for negatively associated sequences. Sci. China Ser. A-Math. 40, 172–182 (1997). https://doi.org/10.1007/BF02874436

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02874436

Keywords

Search

Navigation