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ON THE COMPLETE CONVERGENCE FOR ARRAYS OF ROWWISE EXTENDED NEGATIVELY DEPENDENT RANDOM VARIABLES

  • Qiu, Dehua (School of Mathematics and Computational Science Guangdong University of Business Studies) ;
  • Chen, Pingyan (Department of Mathematics Jinan University) ;
  • Antonini, Rita Giuliano (Dipartimento di Matematica "L. Tonelli" Universita di Pisa) ;
  • Volodin, Andrei (Department of Mathematics and Statistics University of Regina)
  • Received : 2012.04.23
  • Published : 2013.03.01

Abstract

A general result for the complete convergence of arrays of rowwise extended negatively dependent random variables is derived. As its applications eight corollaries for complete convergence of weighted sums for arrays of rowwise extended negatively dependent random variables are given, which extend the corresponding known results for independent case.

Keywords

References

  1. J. Baek and S. T. Park, Convergence of weighted sums for arrays of negatively dependent random variables and its applications, J. Statist. Plann. Inference 140 (2010), no. 9, 2461-2469. https://doi.org/10.1016/j.jspi.2010.02.021
  2. P. Chen, T. C. Hu, X. Liu, and A. Volodin, On complete convergence for arrays of rowwise negatively associated random variables, Theory Probab. Appl. 52 (2008), no. 2, 323-328. https://doi.org/10.1137/S0040585X97983079
  3. A. Gut, On complete convergence in the law of large numbers for subsequences, Ann. Probab. 13 (1985), no. 4, 1286-1291. https://doi.org/10.1214/aop/1176992812
  4. A. Gut , Complete convergence, Asymptotic statistics (Prague, 1993), 237-247, Contrib. Statist., Physica, Heidelberg, 1994.
  5. P. Hsu and H. Robbins, Complete convergence and the law of large numbers, Proc. Nat. Acad. Sci. USA 33 (1947), 25-31. https://doi.org/10.1073/pnas.33.2.25
  6. T.-C. Hu, M. Ordonez Cabrera, S. H. Sung, and A. Volodin, Complete convergence for arrays of rowwise independent random variables, Commun. Korean Math. Soc. 18 (2003), no. 2, 375-383. https://doi.org/10.4134/CKMS.2003.18.2.375
  7. T.-C. Hu, D. Szynal, and A. Volodin, A note on complete convergence for arrays, Statist. Probab. Lett. 38 (1998), no. 1, 27-31. https://doi.org/10.1016/S0167-7152(98)00150-3
  8. T.-C. Hu and A. Volodin, Addendum to "A note on complete convergence for arrays", Statist. Probab. Lett. 47 (2000), no. 2, 209-211. https://doi.org/10.1016/S0167-7152(99)00209-6
  9. K. Joag-Dev and F. Proschan, Negative association of random variables with applications, Ann. Statist. 11 (1983), no. 1, 286-295. https://doi.org/10.1214/aos/1176346079
  10. E. Lehmann, Some concepts of dependence, Ann. Math. Statist. 37 (1966), 1137-1153. https://doi.org/10.1214/aoms/1177699260
  11. L. Liu, Precise large deviations for dependent random variables with heavy tails, Statist. Probab. Lett. 79 (2009), no. 9, 1290-1298. https://doi.org/10.1016/j.spl.2009.02.001
  12. L. Liu, Necessary and sufficient conditions for moderate deviations of dependent random variables with heavy tails, Sci. China Math. 53 (2010), no. 6, 1421-1434. https://doi.org/10.1007/s11425-010-4012-9
  13. W. F. Stout, Almost Sure Convergence, Academic Press, New York, 1974.
  14. S. H. Sung, Complete convergence for weighted sums of random variables, Statist. Probab. Lett. 77 (2007), no. 3, 303-311. https://doi.org/10.1016/j.spl.2006.07.010
  15. S. H. Sung, A note on the complete convergence for arrays of rowwise independent random elements, Statist. Probab. Lett. 78 (2008), no. 11, 1283-1289. https://doi.org/10.1016/j.spl.2007.11.018
  16. S. H. Sung, K. Budsaba, and A. Volodin, Complete convergence for arrays of negatively dependent random variables, To appear in Journal of Mathematical Sciences, New York.
  17. S. H. Sung, A. Volodin, and T.-C. Hu, More on complete convergence for arrays, Statist. Probab. Lett. 71 (2005), no. 4, 303-311. https://doi.org/10.1016/j.spl.2004.11.006
  18. R. L. Taylor, R. Patterson, and A. Bozorgnia, A strong law of large numbers for arrays of rowwise negatively dependent random variables, Stochastic Anal. Appl. 20 (2002), no. 3, 643-656. https://doi.org/10.1081/SAP-120004118
  19. X. J. Wang, T.-C. Hu, A. Volodin, and S. H. Hu, Complete convergence for weighted sums and arrays of rowwise extended negatively dependent random variables, To appear in Communications in Statistics. Theory and Methods.
  20. H. Zarei and H. Jabbari, Complete convergence of weighted sums under negative dependence, Stat Papers doi:10.1007/s00362-009-0238-4.

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