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Strong laws for weighted sums of NA random variables. (English) Zbl 1247.60036
Summary: Strong laws are established for linear statistics that are weighted sums of an negatively associated (NA) random sample. The results obtained not only generalize the results of S. H. Sung [Stat. Probab. Lett. 52, No. 4, 413–419 (2001; Zbl 1020.60016)] to NA random variables, but also extend and sharpen them.

MSC:
60F15 Strong limit theorems
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[1] Bai ZD and 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] Choi BD and Sung SH (1987). Almost sure convergence theorems of weighted sums of random variables. Stoch Anal Appl 5: 365–377 · Zbl 0633.60049 · doi:10.1080/07362998708809124
[3] Chow YS and Teicher H (1997). Probability theory: independence, interchangeability, martingales, 3rd edn. Springer, New York · Zbl 0891.60002
[4] 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
[5] Erdös P (1949). On a theorem of Hsu–Robbins. Ann Math Stat 20: 286–291 · Zbl 0033.29001 · doi:10.1214/aoms/1177730037
[6] Hsu PL and Robbins H (1947). Complete convergence and the law of larege numbers. Proc Natl Acad Sci USA 33(2): 25–31 · Zbl 0030.20101 · doi:10.1073/pnas.33.2.25
[7] Joag DK and Proschan F (1983). Negative associated of random variables with application. Ann Stat 11: 286–295 · Zbl 0508.62041 · doi:10.1214/aos/1176346079
[8] Petrov VV (1995). Limit theorems of probability theory sequences of independent random variables. Oxford Science Publications, Oxford · Zbl 0826.60001
[9] Shao QM (2000). A comparison theorem on moment inequalities between Negatively associated and independent random variables. J Theor Probab 13: 343–356 · Zbl 0971.60015 · doi:10.1023/A:1007849609234
[10] Stout W (1974). Almost sure convergence. Academic, New York · Zbl 0321.60022
[11] Su C, Zhao LC and Wang YB (1996). Moment inequalities and weak convergence for NA sequences. Sci China Ser A 26: 1091–1099
[12] 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
[13] Wu WB (1999). On the strong convergence of a weighted sums. Stat Probab Lett 44: 19–22 · Zbl 0951.60027 · doi:10.1016/S0167-7152(98)00287-9
[14] Yang SC (2000). Moment inequality of random variables partial sums. Sci Chin Ser A 30: 218–223
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