Skip to main content
SpringerLink
Log in

Strong laws for certain types of U-statistics based on negatively associated random variables

  • Published:
Siberian Advances in Mathematics Aims and scope Submit manuscript

Abstract

We establish the Marcinkiewicz-Zygmund-type strong laws of large numbers for certain class of multilinear U-statistics based on negatively associated random variables.

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

Similar content being viewed by others

References

  1. K. Alam and K. M. L. Saxena, “Positive dependence in multivariate distribution,” Commun. Statist. Theory Methods 10(12), 1183–1196 (1981).

    Article  MathSciNet  Google Scholar 

  2. A. D. Barbour, L. Holst, and S. Janson, Poisson Approximation (Oxford University Press, 1992).

  3. B. D. Choi and S. H. Sung, “Almost sure convergence theorems of weighted sums of random variables,” Stoch. Anal. Appl. 5(4), 365–377 (1987).

    Article  MATH  MathSciNet  Google Scholar 

  4. W. Hoeffding, “A class of statistics with asymptotically normal distribution,” Ann. Math. Statist. 19, 293–325 (1948).

    Article  MATH  MathSciNet  Google Scholar 

  5. J. Hoffmann-Jørgensen, “Sums of independent Banach space valued random variables,” Studia Math. 52, 159–186 (1974).

    MathSciNet  Google Scholar 

  6. K. Joag-Dev and F. Proschan, “Negative association of random variables with applications,” Ann. Statist. 11(1), 286–295 (1983).

    Article  MathSciNet  Google Scholar 

  7. V. S. Korolyuk and Yu. V. Borovskikh, Theory of U-statistics (Kluwer Academic Publ., Dordrecht, 1994).

    MATH  Google Scholar 

  8. D. L. Li, M. B. Rao, T. F. Jiang, and X. C. Wang, “Complete convergence and almost sure convergence of weighted sums of random variables,” J. Theor. Probab. 8(1), 49–76 (1995).

    Article  MATH  MathSciNet  Google Scholar 

  9. P. Matula, “A note on the almost sure convergence of sums of negatively dependent random variables,” Statist. Probab. Lett. 15(3), 209–213 (1992).

    Article  MATH  MathSciNet  Google Scholar 

  10. C. M. Newman, “Asymptotic independence and limit theorems for positively and negatively dependent random variables,” in Inequalities in Statistics and Probability (Hayward, California, USA, Institute of Mathematical Statistics, 1984), vol. 5 of IMS Lecture Notes-Monograph Series, pp.127–140.

    Chapter  Google Scholar 

  11. S. Sawyer, “Maximal inequalities of weak type,” Ann. Math. (2) 84, 157–174 (1966).

    Article  MathSciNet  Google Scholar 

  12. Q.M. Shao, “A comparison theorem on moment inequalities between negatively associated and independent random variables,” J. Theoret. Probab. 13(2), 343–356 (2000).

    Article  MATH  MathSciNet  Google Scholar 

  13. Q.M. Shao and C. Su, “The law of the iterated logarithm for negatively associated random variables,” Stoch. Process. Appl. 83(1), 139–148 (1999).

    Article  MATH  MathSciNet  Google Scholar 

  14. W. F. Stout, Almost Sure Convergence (Academic Press, New York, 1974).

    MATH  Google Scholar 

  15. Y.B. Wang, J.G. Yan, F. Y. Cheng, and X.Z. Cai, “On the strong stability for Jamison type weighted product sums of pairwise NQD series with different distribution,” Chinese Ann. Math., A 22(6), 701–706 (2001) [in Chinese].

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Thammasat University Rangsit Center, Pathumthani, 12121, Thailand

    K. Budsaba

  2. Jinan University, Guangzhou, 510630, China

    P. Chen

  3. Silpakorn University, Nakhon Pathom, 73000, Thailand

    K. Panishkan

  4. University of Western Australia, Crawley, WA, 6009, Australia

    A. Volodin

Authors
  1. K. Budsaba
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. K. Panishkan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A. Volodin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Volodin.

Additional information

The text was submitted by the authors in English.

About this article

Cite this article

Budsaba, K., Chen, P., Panishkan, K. et al. Strong laws for certain types of U-statistics based on negatively associated random variables. Sib. Adv. Math. 19, 225–232 (2009). https://doi.org/10.3103/S1055134409040014

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1055134409040014

Key words

Search

Navigation