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A strong limit theorem for weighted sums of sequences of negatively dependent random variables. (English) Zbl 1202.60044

Summary: Applying the moment inequality of negatively dependent random variables which was obtained by N. Asadian et al. [J. Iran. Stat. Soc. JIRSS 5, No. 1–2, 69–75 (2006)], the strong limit theorem for weighted sums of sequences of negatively dependent random variables is discussed. As a result, the strong limit theorem for negatively dependent sequences of random variables is extended. Our results extend and improve the corresponding results of P. D. Bai and P. E. Cheng [Stat. Probab. Lett. 46, No. 2, 105–112 (2000; Zbl 0960.60026)] from the i.i.d. case to ND sequences.

MSC:

60F10 Large deviations

Citations:

Zbl 0960.60026
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References:

[1] Lehmann EL: Some concepts of dependence. Annals of Mathematical Statistics 1966, 37: 1137-1153. 10.1214/aoms/1177699260 · Zbl 0146.40601
[2] Bozorgnia A, Patterson RF, Taylor RL: Limit theorems for ND r.v.’s. University of Georgia; 1993.
[3] Joag-Dev K, Proschan F: Negative association of random variables, with applications. The Annals of Statistics 1983, 11(1):286-295. 10.1214/aos/1176346079 · Zbl 0508.62041
[4] Bozorgnia, A.; Patterson, RF; Taylor, RL, Weak laws of large numbers for negatively dependent random variables in Banach spaces, 11-22 (1996), The Netherlands · Zbl 0883.60009
[5] Amini M: Some contribution to limit theorems for negatively dependent random variable, Ph.D. thesis. 2000.
[6] Fakoor V, Azarnoosh HA: Probability inequalities for sums of negatively dependent random variables. Pakistan Journal of Statistics 2005, 21(3):257-264. · Zbl 1129.60303
[7] Nili Sani HR, Amini M, Bozorgnia A: Strong laws for weighted sums of negative dependent random variables. Islamic Republic of Iran. Journal of Sciences 2005, 16(3):261-266.
[8] Klesov O, Rosalsky A, Volodin AI: On the almost sure growth rate of sums of lower negatively dependent nonnegative random variables. Statistics & Probability Letters 2005, 71(2):193-202. 10.1016/j.spl.2004.10.027 · Zbl 1070.60030
[9] Wu QY, Jiang YY: Strong consistency of M estimator in linear model for negatively dependent random samples. Communications in Statistics: Theory and Methods, accepted · Zbl 1208.62039
[10] Wu, QY, Complete convergence for negatively dependent sequences of random variables, No. 2010 (2010) · Zbl 1202.60050
[11] Wu, QY; Jiang, YY, Some strong limit theorems for weighted product sums of [InlineEquation not available: see fulltext.]-mixing sequences of random variables, No. 2009 (2009)
[12] Chen PY, Gan SX: Limiting behavior of weighted sums of i.i.d. random variables. Statistics & Probability Letters 2007, 77(16):1589-1599. 10.1016/j.spl.2007.03.038 · Zbl 1131.60020
[13] Bai ZD, Cheng PE: Marcinkiewicz strong laws for linear statistics. Statistics & Probability Letters 2000, 46(2):105-112. 10.1016/S0167-7152(99)00093-0 · Zbl 0960.60026
[14] Asadian N, Fakoor V, Bozorgnia A: Rosenthal’s type inequalities for negatively orthant dependent random variables. Journal of the Iranian Statistical Society 2006, 5: 69-75. · Zbl 1490.60044
[15] Wu QY: Probability Limit Theory for Mixed Sequence. Science Press, Beijing, China; 2006.
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