×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite
Full Text: DOI
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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.