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On the strong convergence for weighted sums of random variables. (English) Zbl 1247.60041

Summary: 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 G.-H. Cai [Metrika 68, No. 3, 323–331 (2008; Zbl 1247.60036)].

MSC:

60F15 Strong limit theorems
62G05 Nonparametric estimation

Citations:

Zbl 1247.60036
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References:

[1] Bai ZD, Cheng PE (2000) Marcinkiewicz strong laws for linear statistics. Stat Probab Lett 46: 105–112 · Zbl 0960.60026
[2] Cai GH (2008) Strong laws for weighted sums of NA random variables. Metrika 68: 323–331 · Zbl 1247.60036
[3] Chen P, Gan S (2007) Limiting behavior of weighted sums of i.i.d. random variables. Stat Probab Lett 77: 1589–1599 · Zbl 1131.60020
[4] 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
[5] Cuzick J (1995) A strong law for weighted sums of i.i.d. random variables. J Theor Probab 8: 625–641 · Zbl 0833.60031
[6] Erdös P (1949) On a theorem of Hsu and Robbins. Ann Math Stat 20: 286–291 · Zbl 0033.29001
[7] Hsu PL, Robbins H (1947) Complete convergence and the law of large numbers. Proc Nat Acad Sci USA 33: 25–31 · Zbl 0030.20101
[8] Joag-Dev K, Proschan F (1983) Negative association of random variables with applications. Ann Stat 11: 286–295 · Zbl 0508.62041
[9] Sung SH (2001) Strong laws for weighted sums of i.i.d. random variables. Stat Probab Lett 52: 413–419 · Zbl 1020.60016
[10] Wu WB (1999) On the strong convergence of a weighted sum. Stat Probab Lett 44: 19–22 · Zbl 0951.60027
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