Equivalent conditions of the complete convergence for weighted sums of NSD random variables

References

• Adler, A., and A. Rosalsky. 1987. Some general strong laws for weighted sums of stochastically dominated random variables. Stochastic Analysis and Applications 5 (1):1–16.
   Web of Science ®Google Scholar
• Adler, A., A. Rosalsky, and R. L. Taylor. 1989. Strong laws of large numbers for weighted sums of random variables in normed linear spaces. International Journal of Mathematics and Mathematical Sciences 12 (3):507–30.
   Google Scholar
• Alam, K., and K. M. L. Saxena. 1981. Positive dependence in multivariate distributions. Communications in Statistics—Theory and Methods 10 (12):1183–96.
   Web of Science ®Google Scholar
• Bai, Z. D., and C. Su. 1985. The complete convergence for partial sums of i.i.d. random variables. Science in China Series A: Mathematics 28 (12):1261–77.
   Google Scholar
• Baum, L. E., and M. Katz. 1965. Convergence rates in the law of large numbers. Transactions of the American Mathematical Society 120 (1):108–23.
   Web of Science ®Google Scholar
• Christofides, T. C., and E. Vaggelatou. 2004. A connection between supermodular ordering and positive/negative association. Journal of Multivariate Analysis 88 (1):138–51.
   Web of Science ®Google Scholar
• Deng, X., X. J. Wang, Y. Wu, and Y. Ding. 2016. Complete moment convergence and complete convergence for weighted sums of NSD random variables. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas 110 (1):97–120.
   Google Scholar
• Eghbal, N., M. Amini, and A. Bozorgnia. 2010. Some maximal inequalities for quadratic forms of negative superadditive dependence random variables. Statistics & Probability Letters 80 (7–8):587–91.
   Web of Science ®Google Scholar
• Eghbal, N., M. Amini, and A. Bozorgnia. 2011. On the Kolmogorov inequalities for quadratic forms of dependent uniformly bounded random variables. Statistics & Probability Letters 81 (8):1112–20.
   Web of Science ®Google Scholar
• Erdös, P. 1949. On a theorem of HSU and Robbins. The Annals of Mathematical Statistics 20 (2):286–91.
   Google Scholar
• Hsu, P. L., and H. Robbins. 1947. Complete convergence and the law of large numbers. Proceedings of the National Academy of Sciences of the United States of America 33 (2):25–31.
   PubMed Web of Science ®Google Scholar
• Hu, T. Z. 2000. Negatively superadditive dependence of random variables with applications. Chinese Journal of Applied Probability and Statistics 16:133–44.
   Google Scholar
• Joag-Dev, K., and F. Proschan. 1983. Negative association of random variables with applications. The Annals of Statistics 11 (1):286–95.
   Web of Science ®Google Scholar
• Kemperman, J. H. B. 1977. On the FKG-inequalities for measures on a partially ordered space. Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen 80 (4):313–31.
   Google Scholar
• Meng, B., D. C. Wang, and Q. Y. Wu. 2018. Complete convergence and complete moment convergence for arrays of rowwise negatively superadditive dependent random variables. Communications in Statistics—Theory and Methods 47 (16):3910–22.
   Web of Science ®Google Scholar
• Naderi, H., M. Amini, and A. Bozorgnia. 2017. On the rate of complete convergence for weighted sums of NSD random variables and an application. Applied Mathematics-A Journal of Chinese Universities 32 (3):270–80.
   Google Scholar
• Shen, A. T., and X. H. Wang. 2015. Kaplan-Meier estimator and hazard estimator for censored negatively superadditive dependent data. Statistics 50 (2):1–388.
   Web of Science ®Google Scholar
• Shen, A. T., M. X. Xue, and A. Volodin. 2016. Complete moment convergence for arrays of NSD random variables. Stochastics 88 (4):606–21.
   Web of Science ®Google Scholar
• Shen, A. T., Y. Zhang, and A. Volodin. 2015. Applications of the rosenthal-type inequality for negatively superadditive dependent random variables. Metrika 78 (3):295–311.
   Web of Science ®Google Scholar
• Shen, Y., X. J. Wang, and S. H. Hu. 2013. On the strong convergence and some inequalities for negatively superadditive dependent sequences. Journal of Inequalities and Applications 2013 (1):448–11.
   Google Scholar
• Shen, Y., X. J. Wang, W. Z. Yang, and S. H. Hu. 2013. Almost sure convergence theorem and strong stability for weighted sums of NSD random variables. Acta Mathematica Sinica, English Series 29 (4):743–56.
   Web of Science ®Google Scholar
• Wang, X. J., A. T. Shen, Z. Y. Chen, and S. H. Hu. 2015. Complete convergence for weighted sums of NSD random variables and its application in the EV regression model. Test 24 (1):166–84.
   Web of Science ®Google Scholar
• Wang, X. J., and Y. Wu. 2017. On complete convergence and complete moment convergence for a class of random variables. Journal of the Korean Mathematical Society 54 (3):877–96.
   Web of Science ®Google Scholar
• Wang, X. J., X. Deng, L. L. Zheng, and S. H. Hu. 2014. Complete convergence for arrays of rowwise negatively superadditive dependent random variables and its applications. Statistics 48 (4):834–50.
   Web of Science ®Google Scholar
• Wang, X. J., Y. Wu, and S. H. Hu. 2018. Strong and weak consistency of LS estimators in the EV regression model with negatively superadditive-dependent errors. AStA Advances in Statistical Analysis 102 (1):41–65.
   Web of Science ®Google Scholar
• Wu, Y., X. J. Wang, and S. H. Hu. 2016. Complete convergence for arrays of rowwise negatively superadditive-dependent random variables and its applications. Applied Mathematics: A Journal of Chinese Universities 31 (4):439–57.
   Google Scholar
• Xue, Z., L. L. Zhang, Y. J. Lei, and Z. G. Chen. 2015. Complete moment convergence for weighted sums of negatively superadditive dependent random variables. Journal of Inequalities and Applications 2015 (1):1–13.
   Google Scholar
• Zhou, X. C. 2010. Complete moment convergence of moving average processes under φ-mixing assumptions. Statistics & Probability Letters 80 (5–6):285–92.
   Web of Science ®Google Scholar