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).
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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
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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
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DOI: https://doi.org/10.1007/s00362-009-0241-9