Abstract
A strong convergence result is obtained for weighted sums of identically distributed negatively associated random variables which have a suitable moment condition. This result improves the result of Cai (Metrika 68:323–331, 2008).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bai ZD, Cheng PE (2000) Marcinkiewicz strong laws for linear statistics. Stat Probab Lett 46: 105–112
Cai GH (2008) Strong laws for weighted sums of NA random variables. Metrika 68: 323–331
Chen P, Gan S (2007) Limiting behavior of weighted sums of i.i.d. random variables. Stat Probab Lett 77: 1589–1599
Chen P, Hu TC, Liu X, Volodin A (2007) On complete convergence for arrays of rowwise negatively associated random variables. Theory Probab Appl 52: 1–5
Cuzick J (1995) A strong law for weighted sums of i.i.d. random variables. J Theor Probab 8: 625–641
Erdös P (1949) On a theorem of Hsu and Robbins. Ann Math Stat 20: 286–291
Hsu PL, Robbins H (1947) Complete convergence and the law of large numbers. Proc Nat Acad Sci USA 33: 25–31
Joag-Dev K, Proschan F (1983) Negative association of random variables with applications. Ann Stat 11: 286–295
Sung SH (2001) Strong laws for weighted sums of i.i.d. random variables. Stat Probab Lett 52: 413–419
Wu WB (1999) On the strong convergence of a weighted sum. Stat Probab Lett 44: 19–22
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Sung, S.H. On the strong convergence for weighted sums of random variables. Stat Papers 52, 447–454 (2011). https://doi.org/10.1007/s00362-009-0241-9
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00362-009-0241-9