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Original Articles

Complete moment convergence of weighted sums for arrays of negatively dependent random variables and its applications

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Pages 3185-3195 | Received 21 Oct 2012, Accepted 19 Feb 2014, Published online: 28 Apr 2016

References

  • Baek, J.I., Ko, M.H., Kim, T.S. (2008). On the complete convergence for weighted sums of dependent random variables under condition of weighted integrability. J. Kor. Math. Soc. 45:1101–1111.
  • Baek, J.I., Park, S.T. (2010). Convergence of weighted sums for arrays of negatively dependent random variables and its applications. J. Statist. Plann. Infer. 140:2461–2469.
  • Bozorgnia, A., Patterson, R.F., Taylor, R.L. (1996). Limit theorems for dependent random variables. World Congress Nonlin. Anal. 92 11:1639–1650.
  • Burton, R.M., Dehling, H. (1990). Large deviations for some weakly dependent random processes. Statist. Probab. Lett. 9:397–401.
  • Chow, Y.S. (1988). On the rate of moment complete convergence of sample sums and extremes. Bulletin of the Bull. Inst. Math. Academia Sinica. 16:177–201.
  • Ebrahimi, N., Ghosh, M. (1981). Multivariate negative dependence. Commun. Statist. Theor. Meth. 10:307–337.
  • Gan, S.X., Chen, P.Y. (2008). Some limit theorems for sequences of pairwise NQD random variables. Acta Math. Sci., Ser. B, Engl. Ed. 28:269–281.
  • Gan, S.X., Chen, P.Y. (2008). Strong convergence rate of weighted sums for NOD sequences. Acta Math. Sci., Ser. A 28:283–290 ( in Chinese).
  • Hsu, P.L., Robbins, H. (1947). Complete convergence and the law of large numbers. Proc. Nat. Acad. Sci. 33:25–31.
  • Ko, M.H., Han, K.H., Kim, T.S. (2006). Strong laws of large numbers for weighted sums of negatively dependent random variables. J. Kor. Math. Soc. 43(6):1325–1338.
  • Lehmann, E.L. (1966). Some concepts of dependence. Ann. Math. Statist. 37:1137–1153.
  • Li, R., Yang, W.G. (2008). Strong convergence of pairwise NQD random sequences. J. Math. Anal. Appl. 344:741–747.
  • Liang, H.Y., Chen, Z.J., Su, C. (2002). Convergence of Jamison-type weighted sums of pairwise negatively quadrant dependent random variables. Acta Math. Appl. Sin. Engl. Ser. 18:161–168.
  • Matula, P. (1992). A note on the almost sure convergence of sums of negatively dependent random variables. Statist. Probab. Lett. 15:209–213.
  • Meng, Y. J., Lin, Z.Y. (2009). On the weak laws of large numbers for arrays of random variables. Statist. Probab. Lett. 79:2405–2414.
  • Ordóñez, Cabrera, M., Volodin, A. (2005). Mean convergence theorems and weak laws of large numbers for weighted sums of random variables under a condition of weighted integrability. J. Math. Anal. Appl. 305:644–658.
  • Qiu, D. H., Chan, K.C., Antonini, R.G., Volodin, A. (2010). On the strong rates of convergence for arrays of rowwise negatively dependent random variables. Stoch. Anal. Appl. 29:375–385.
  • Sung, H.S. (2013). Convergence in r-mean of weighted sums of NQD random variables. Appl. Math. Lett. 26:18–24.
  • Sung, H.S., Lisawadi, S., Volodin, A. (2008). Weak laws of large numbers for arrays under a condition of uniform integrability. J. Kor. Math. Soc. 45:289–300.
  • Taylor, R.L., Patterson, R.F., Bozorgnia, A. (2002). A strong law of large numbers for arrays of rowwise negatively dependent random variables. Stoch. Anal. Appl. 20(3):643–656.
  • Taylor, R.L., Patterson, R.F., Bozorgnia, A. (2001). Weak laws of large numbers for arrays of rowwise negatively dependent random variables. J. Appl. Math. Stoch. Anal. 14(3):227–236.
  • Volodin, A. (2002). On the Kolmogorov exponential inequality for negatively dependent random variables. Pak. J. Statist. 18(2):249–253.
  • Volodin, A., Cabrera, M.O., Hu, T.C. (2006). Convergence rate of the dependent bootstrapped means. Theor. Probab. Appl. 50(2):337–346.
  • Wu, Q.Y. (2002). Convergence properties of pairwise NQD random sequences. Acta Math. Sin. Engl. Ser. 45:617–624 ( in Chinese).
  • Wu, Y.F., Cabrera, M.O., Volodin, A. (2012). On limiting behavior for arrays of rowwise negatively orthant dependent random variables. J. Kor. Statist. Soc., doi:10.1016/j.jkss.2012.05.001.
  • Wu, Y.F., Guan, M. (2011). Mean convergence theorems and weak laws of large numbers for weighted sums of dependent random variables. J. Math. Anal. Appl. 377:613–623.
  • Wu, Y.F., Wang, D.C. (2012). Convergence properties for arrays of rowwise pairwise negatively quadrant dependent random variables. Appl. Math., Praha 57:463–476.
  • Wu, Y.F., Zhu, D.J. (2010). Convergence properties of partial sums for arrays of rowwise negatively orthant dependent random variables. J. Kor. Statist. Soc. 39:189–197.

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