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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:
60F15Strong limit theorems
62G05Nonparametric estimation
References:
[1]Bai ZD, Cheng PE (2000) Marcinkiewicz strong laws for linear statistics. Stat Probab Lett 46: 105–112 · Zbl 0960.60026 · doi:10.1016/S0167-7152(99)00093-0
[2]Cai GH (2008) Strong laws for weighted sums of NA random variables. Metrika 68: 323–331 · Zbl 1247.60036 · doi:10.1007/s00184-007-0160-5
[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 · doi:10.1016/j.spl.2007.03.038
[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 · doi:10.1007/BF02218047
[6]Erdös P (1949) On a theorem of Hsu and Robbins. Ann Math Stat 20: 286–291 · Zbl 0033.29001 · doi:10.1214/aoms/1177730037
[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 · doi:10.1073/pnas.33.2.25
[8]Joag-Dev K, Proschan F (1983) Negative association of random variables with applications. Ann Stat 11: 286–295 · Zbl 0508.62041 · doi:10.1214/aos/1176346079
[9]Sung SH (2001) Strong laws for weighted sums of i.i.d. random variables. Stat Probab Lett 52: 413–419 · Zbl 1020.60016 · doi:10.1016/S0167-7152(01)00020-7
[10]Wu WB (1999) On the strong convergence of a weighted sum. Stat Probab Lett 44: 19–22 · Zbl 0951.60027 · doi:10.1016/S0167-7152(98)00287-9