Table of Contents Author Guidelines Submit a Manuscript
The Scientific World Journal
Volume 2014, Article ID 478612, 7 pages
http://dx.doi.org/10.1155/2014/478612
Research Article

Complete Moment Convergence and Mean Convergence for Arrays of Rowwise Extended Negatively Dependent Random Variables

1College of Mathematics and Computer Science, Tongling University, Tongling 244000, China
2Department of Mathematics and Physics, Anhui Traditional Chinese Medical College, Hefei 230051, China

Received 29 August 2013; Accepted 19 December 2013; Published 5 February 2014

Academic Editors: S. Chen and T. Prieto-Rumeau

Copyright © 2014 Yongfeng Wu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. P. L. Hsu and H. Robbins, “Complete convergence and the law of large numbers,” Proceedings of the National Academy of Sciences of the United States of America, vol. 33, pp. 25–31, 1947. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. Y. S. Chow, “On the rate of moment convergence of sample sums and extremes,” Bulletin of the Institute of Mathematics. Academia Sinica, vol. 16, no. 3, pp. 177–201, 1988. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. N. Ebrahimi and M. Ghosh, “Multivariate negative dependence,” Communications in Statistics A, vol. 10, no. 4, pp. 307–337, 1981. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. L. Liu, “Precise large deviations for dependent random variables with heavy tails,” Statistics and Probability Letters, vol. 79, no. 9, pp. 1290–1298, 2009. View at Publisher · View at Google Scholar · View at Scopus
  5. K. Joag-Dev and F. Proschan, “Negative association of random variables, with applications,” The Annals of Statistics, vol. 11, no. 1, pp. 286–295, 1983. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. R. L. Taylor, R. F. Patterson, and A. Bozorgnia, “A strong law of large numbers for arrays of rowwise negatively dependent random variables,” Stochastic Analysis and Applications, vol. 20, no. 3, pp. 643–656, 2002. View at Publisher · View at Google Scholar · View at Scopus
  7. M.-H. Ko and T.-S. Kim, “Almost sure convergence for weighted sums of negatively orthant dependent random variables,” Journal of the Korean Mathematical Society, vol. 42, no. 5, pp. 949–957, 2005. View at Google Scholar · View at Scopus
  8. M.-H. Ko, K.-H. Han, and T.-S. Kim, “Strong laws of large numbers for weighted sums of negatively dependent random variables,” Journal of the Korean Mathematical Society, vol. 43, no. 6, pp. 1325–1338, 2006. View at Google Scholar · View at Scopus
  9. Y. F. Wu, M. Ordóñez-Cabrera , and A. Volodin, “On limiting behavior for arrays of rowwise negatively orthant dependent random variables,” Journal of the Korean Statistical Society, vol. 42, pp. 61–70, 2013. View at Google Scholar
  10. M. Amini D. and A. Bozorgnia, “Complete convergence for negatively dependent random variables,” Journal of Applied Mathematics and Stochastic Analysis, vol. 16, no. 2, pp. 121–126, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  11. S. X. Gan and P. Y. Chen, “Strong convergence rate of weighted sums for negatively orthant dependent sequences,” Acta Mathematica Scientia A, vol. 28, no. 2, pp. 283–290, 2008 (Chinese). View at Google Scholar · View at MathSciNet
  12. Q. Wu, “Complete convergence for negatively dependent sequences of random variables,” Journal of Inequalities and Applications, vol. 2010, Article ID 507293, 10 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. Y.-F. Wu and D.-J. Zhu, “Convergence properties of partial sums for arrays of rowwise negatively orthant dependent random variables,” Journal of the Korean Statistical Society, vol. 39, no. 2, pp. 189–197, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  14. Q. Dehua, K.-C. Chang, R. Giuliano Antonini, and A. Volodin, “On the strong rates of convergence for arrays of rowwise negatively dependent random variables,” Stochastic Analysis and Applications, vol. 29, no. 3, pp. 375–385, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. A. T. Shen, “On the strong convergence rate for weighted sums of arrays of rowwise negatively orthant dependent random variables,” Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales A, vol. 107, pp. 257–271, 2012. View at Publisher · View at Google Scholar
  16. Y. Chen, A. Chen, and K. W. Ng, “The strong law of large numbers for extended negatively dependent random variables,” Journal of Applied Probability, vol. 47, no. 4, pp. 908–922, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. Y. Wu and M. Guan, “Convergence properties of the partial sums for sequences of end random variables,” Journal of the Korean Mathematical Society, vol. 49, no. 6, pp. 1097–1110, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. D. Qiu, P. Chen, R. G. Antonini, and A. Volodin, “On the complete convergence for arrays of rowwise extended negatively dependent random variables,” Journal of the Korean Mathematical Society, vol. 50, no. 2, pp. 379–392, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. T.-C. Hu and R. L. Taylor, “On the strong law for arrays and for the bootstrap mean and variance,” International Journal of Mathematics and Mathematical Sciences, vol. 20, no. 2, pp. 375–382, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. S. H. Sung, “Complete convergence for sums of arrays of random elements,” International Journal of Mathematics and Mathematical Sciences, vol. 23, no. 11, pp. 789–794, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. S. Gan and P. Chen, “On the limiting behavior of the maximum partial sums for arrays of rowwise NA random variables,” Acta Mathematica Scientia B, vol. 27, no. 2, pp. 283–290, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet