Complete convergence for negatively orthant dependent random variables

详细信息    查看全文

• 作者：Dehua Qiu (7)
  Qunying Wu (8)
  Pingyan Chen (9)
  
  7. School of Mathematics and Statistics ; Guangdong University of Finance and Economics ; Guangzhou ; 510320 ; P.R. China
  8. College of Science ; Guilin University of Technology ; Guilin ; 541004 ; P.R. China
  9. Department of Mathematics ; Jinan University ; Guangzhou ; 510630 ; P.R. China
  
• 关键词：NOD ; complete convergence
• 刊名：Journal of Inequalities and Applications
• 出版年：2014
• 出版时间：December 2014
• 年：2014
• 卷：2014
• 期：1
• 全文大小：208 KB
• 参考文献：1. Hsu, P, Robbins, H (1947) Complete convergence and the law of large numbers. Proc. Natl. Acad. Sci. USA 33: pp. 25-31 CrossRef
  2. Baum, IE, Katz, M (1965) Convergence rates in the law of large numbers. Trans. Am. Math. Soc 120: pp. 108-123 CrossRef
  3. Baek, J, Park, ST (2010) Convergence of weighted sums for arrays of negatively dependent random variables and its applications. J. Stat. Plan. Inference 140: pp. 2461-2469 CrossRef
  4. Bai, ZD, Su, C (1985) The complete convergence for partial sums of i.i.d. random variables. Sci. China Ser. A 5: pp. 399-412
  5. Chen, P, Hu, TC, Liu, X, Volodin, A (2007) On complete convergence for arrays of rowwise negatively associated random variables. Theory Probab. Appl 52: pp. 323-328 CrossRef
  6. Gan, S, Chen, P (2008) Strong convergence rate of weighted sums for negatively dependent sequences. Acta. Math. Sci. Ser.聽A 28: pp. 283-290
  7. Gut, A (1992) Complete convergence for arrays. Period. Math. Hung 25: pp. 51-75 CrossRef
  8. Kuczmaszewska, A (2010) On complete convergence in Marcinkiewica-Zygmund type SLLN for negatively associated random variables. Acta Math. Hung 128: pp. 116-130 CrossRef
  9. Liang, HY, Wang, L (2001) Convergence rates in the law of large numbers for B-valued random elements. Acta Math. Sci. Ser.聽B 21: pp. 229-236
  10. Peligrad, M, Gut, A (1999) Almost-sure results for a class of dependent random variables. J. Theor. Probab 12: pp. 87-104 CrossRef
  11. Qiu, DH, Chang, KC, Antonini, RG, Volodin, A (2011) On the strong rates of convergence for arrays of rowwise negatively dependent random variables. Stoch. Anal. Appl 29: pp. 375-385 CrossRef
  12. Sung, SH (2007) Complete convergence for weighted sums of random variables. Stat. Probab. Lett 77: pp. 303-311 CrossRef
  13. Sung, SH (2008) A note on the complete convergence for arrays of rowwise independent random elements. Stat. Probab. Lett 78: pp. 1283-1289 CrossRef
  14. Taylor, RL, Patterson, R, Bozorgnia, A (2002) A strong law of large numbers for arrays of rowwise negatively dependent random variables. Stoch. Anal. Appl 20: pp. 643-656 CrossRef
  15. Wang, XM (1999) Complete convergence for sums of NA sequence. Acta Math. Appl. Sin 22: pp. 407-412
  16. Zhang, LX, Wang, JF (2004) A note on complete convergence of pairwise NQD random sequences. Appl. Math. J. Chin. Univ. Ser. A 19: pp. 203-208 CrossRef
  17. Shao, QM (2000) A comparison theorem on moment inequalities between negatively associated and independent random variables. J. Theor. Probab 13: pp. 343-356 CrossRef
  18. Joag-Dev, K, Proschan, F (1983) Negative association of random variables with applications. Ann. Stat 11: pp. 286-295 CrossRef
  19. Bozorgnia, A, Patterson, RF, Taylor, RL (1996) Limit theorems for dependent random variables. Proc. of the First World Congress of Nonlinear Analysts 鈥?2. de Gruyter, Berlin, pp. 1639-1650
  20. Ko, MH, Han, KH, Kim, TS (2006) Strong laws of large numbers for weighted sums of negatively dependent random variables. J. Korean Math. Soc 43: pp. 1325-1338 CrossRef
  21. Ko, MH, Kim, TS (2005) Almost sure convergence for weighted sums of negatively dependent random variables. J. Korean Math. Soc 42: pp. 949-957 CrossRef
  22. Asadian, N, Fakoor, V, Bozorgnia, A (2006) Rosenthal鈥檚 type inequalities for negatively orthant dependent random variables. J. Iran. Stat. Soc 5: pp. 69-75
  23. Stout, WF (1974) Almost Sure Convergence. Academic Press, New York
  24. Seneta, E (1976) Lecture Notes in Math. 508. Regularly Varying Function. Springer, Berlin CrossRef
  
• 刊物主题：Analysis; Applications of Mathematics; Mathematics, general;
• 出版者：Springer International Publishing
• ISSN：1029-242X

文摘

In this paper, necessary and sufficient conditions of the complete convergence are obtained for the maximum partial sums of negatively orthant dependent (NOD) random variables. The results extend and improve those in Kuczmaszewska (Acta Math. Hung. 128(1-2):116-130, 2010) for negatively associated (NA) random variables. MSC: 60F15, 60G50.