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Original Articles

Strong law of large numbers and complete convergence for non-identically distributed WOD random variables

, &
Pages 2687-2699 | Received 12 Dec 2017, Accepted 30 Apr 2018, Published online: 10 Feb 2019

References

  • Block, H., T. Savits, and M. Shaked. 1982. Some concept of negative dependence. Annals of Probability 10:765–72. doi: 10.1214/aop/1176993784.
  • Chen, Y., A. Chen, and K. Ng. 2010. The strong law of large numbers for extend negatively dependent random variables. Journal of Applied Probability 47:908–22. doi: 10.1239/jap/1294170508.
  • Chen, Y., K. Yuen, and K. Ng. 2011. Precise large deviations of random sums in presence of negative dependence and consistent variation. Methodology and Computing in Applied Probability 13:821–33. doi: 10.1007/s11009-010-9194-7.
  • Chen, W., Y. Wang, and D. Cheng. 2016. An inequality of widely dependent random variables and its applications, Lithuanian Mathematical Journal 56:16–31. doi: 10.1007/s10986-016-9301-8.
  • Ebrahimi, N., and M. Ghosh. 1981. Multivariate negative dependence. Communications in Statistics—Theory and Methods 10:307–37. doi: 10.1080/03610928108828041.
  • Fuk, D., and S. Nagaev. 1971. Probabilistic inequalities for sums of independent random variables, Teor. Veroyatn. Primen. 16:660–75 (in Russian). English transl., Theory of Probability and Its Applications 16:643–60. doi: 10.1137/1116071.
  • He, W., D. Cheng, and Y. Wang. 2013. Asymptotic lower bounds of precise large deviations with nonnegative and dependent random variables. Statistics & Probability Letters 83:331–38. doi: 10.1016/j.spl.2012.09.019.
  • Joag-Dev, K., and F. Proschan. 1983. Negative association of random variables with applications. Annals of Statistics 11:286–95. doi: 10.1214/aos/1176346079.
  • Liu, L. 2009. Precise large deviations for dependent random variables with heavy tails. Statistics & Probability Letters 79:1290–98. doi: 10.1016/j.spl.2009.02.001.
  • Liu, L. 2010. Necessary and sufficient conditions for moderate deviations of dependent random variables with heavy tails. Science in China. Series A, Mathematics 53:1421–34. doi: 10.1007/s11425-010-4012-9.
  • Liu, X., Q. Gao, and Y. Wang. 2012. A note on a dependent risk model with constant interest rate. Statistics & Probability Letters 82:707–12. doi: 10.1016/j.spl.2011.12.016.
  • Nagaev, S. 1979. Large deviations of sums of independent random variables. Annals of Probability 7:745–89. doi: 10.1214/aop/1176994938.
  • Shen, A. 2013. Bernstein-type inequality for widely dependent sequence and its application to nonparametric regression models. Abstract and Applied Analysis 2013:1–9. doi: 10.1155/2013/862602.
  • Shen, A. 2014. On asymptotic approximation of inverse moments for a class of nonnegative random variables. Statistics 48:1371–79. doi: 10.1080/02331888.2013.801480.
  • Sung, S. 2011. On the exponential inequalities for negatively dependent random variables. Journal of Mathematical Analysis and Applications 381:538–45. doi: 10.1016/j.jmaa.2011.02.058.
  • Tang, Q. 2006. Insensitivity to negative dependence of the asymptotic behavior of precise large deviation. Electronic Journal of Probability 11:107–20. doi: 10.1214/EJP.v11-304.
  • Wang, K., Y. Wang, and Q. Gao. 2013. Uniform asymptotics for the finite-time ruin probability of a dependent risk model with a constant interest rate. Methodology and Computing in Applied Probability 15:109–24. doi: 10.1007/s11009-011-9226-y.
  • Wang, S., and X. Wang. 2013. Precise large deviations for random sums of END real-valued random variables with consistent variation. Journal of Mathematical Analysis and Applications 402:660–67. doi: 10.1016/j.jmaa.2013.02.002.
  • Wang, X., S. Hu, A. Shen, and W. Yang. 2011. An exponential inequality for a NOD sequence and a strong law of large numbers. Applied Mathematics Letters 24:219–23. doi: 10.1016/j.aml.2010.09.007.
  • Wang, X., S. Hu, and A. Volodin. 2011. Strong limit theorems for weighted sums of NOD sequence and exponential inequalities. Bulletin of the Korean Mathematical Society 48:923–38. doi: 10.4134/BKMS.2011.48.5.923.
  • Wang, X., C. Xu, T. Hu, A. Volodin, and S. Hu. 2014. On complete convergence for widely orthant-dependent random variables and its applications in nonparametric regression models. TEST 23:607–29. doi: 10.1007/s11749-014-0365-7.
  • Wang, Y., and D. Cheng. 2011. Basic renewal theorems for a random walk with widely dependent increments and their applications. Journal of Mathematical Analysis and Applications 384:597–606. doi: 10.1016/j.jmaa.2011.06.010.
  • Wang, Y., Z. Cui, K. Wang, and X. Ma. 2012. Uniform asymptotics of the finite-time ruin probability for all times. Journal of Mathematical Analysis and Applications 390:208–23. doi: 10.1016/j.jmaa.2012.01.025.
  • Wu, Q., and Y. Jiang. 2011. The strong consistency of M estimator in a linear model for negatively dependent random samples. Communications in Statistics—Theory and Methods 40:467–91. doi: 10.1080/03610920903427792.

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