Advanced search
Publication Cover
Communications in Statistics - Theory and Methods Volume 41, 2012 - Issue 9
Submit an article Journal homepage
98
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

On Complete Convergence for Arrays of Dependent Random Variables

Soo Hak Sung Department of Applied Mathematics, Pai Chai University, Taejon, South KoreaCorrespondence[email protected]
Pages 1663-1674 | Received 22 Jul 2010, Accepted 09 Dec 2010, Published online: 28 Mar 2012

References

  • Alam , K. , Saxena , K. M. L. ( 1981 ). Positive dependence in multivariate distributions . Commun. Statist. Theor. Meth. 10 : 1183 – 1196 .
  • Chen , P. , Hu , T.-C. , Liu , X. , Volodin , A. ( 2007 ). On complete convergence for arrays of rowwise negatively associated random variables . Theor. Probab. Appl. 52 : 393 – 397 .
  • Ebrahimi , N. , Ghosh , M. ( 1981 ). Multivariate negative dependence . Commun. Statist. Theor. Meth. 10 : 307 – 337 .
  • Erdös , P. ( 1949 ). On a theorem of Hsu and Robbins . Ann. Math. Statist. 20 : 286 – 291 .
  • Fakoor , V. , Azarnoosh , H. A. ( 2005 ). Probability inequalities for sums of negatively dependent random variables . Pak. J. Statist. 21 : 257 – 264 .
  • Hoffmann-Jørgensen, J. ( 1974 ). Sums of independent Banach space valued random variables . Studia Math. 52 : 159 – 186 .
  • Hsu , P. L. , Robbins , H. ( 1947 ). Complete convergence and the law of large numbers . Proc. Nat. Acad. Sci. USA 33 : 25 – 31 .
  • Hu , T.-C. , Volodin , A. ( 2000 ). Addendum to “A note on complete convergence for arrays” Statist . Probab. Lett. 38(1):27–31. Statist. Probab. Lett. 47 : 209 – 211 .
  • Hu , T.-C. , Ordó\~ nez Cabrera , M. , Sung , S. H. , Volodin , A. ( 2003 ). Complete convergence for arrays of rowwise independent random variables . Commun. Korean Math. Soc. 18 : 375 – 383 .
  • Hu , T.-C. , Szynal , D. , Volodin , A. ( 1998 ). A note on complete convergence for arrays . Statist. Probab. Lett. 38 : 27 – 31 .
  • Joag-Dev , K. , Proschan , F. ( 1983 ). Negative association of random variables, with applications . Ann. Statist. 11 : 286 – 295 .
  • Kruglov , V. M. , Volodin , A. I. , Hu , T.-C. ( 2006 ). On complete convergence for arrays . Statist. Probab. Lett. 76 : 1631 – 1640 .
  • Kuczmaszewska , A. ( 2004 ). On some conditions for complete convergence for arrays . Statist. Probab. Lett. 66 : 399 – 405 .
  • Shao , Q.-M. ( 2000 ). A comparison theorem on moment inequalities between negatively associated and independent random variables . J. Theor. Probab. 13 : 343 – 356 .
  • Sung , S. H. , Urmeneta , H. , Volodin , A. I. ( 2008 ). On complete convergence for arrays of random elements . Stochastic Anal. Appl. 26 : 595 – 602 .
  • Sung , S. H. , Volodin , A. I. , Hu , T.-C. ( 2005 ). More on complete convergence for arrays . Statist. Probab. Lett. 71 : 303 – 311 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.