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Complete convergence for weighted sums of negatively dependent random variables. (English) Zbl 1314.62096
Summary: In this paper, we obtain a complete convergence result for weighted sums of negatively dependent random variables under mild conditions of weights. This result generalizes and improves the result of {\it H. Zarei} and {\it H. Jabbari Nooghabi} [Stat. Pap. 52, No. 2, 413--418 (2011; Zbl 1247.60044)]. Our result also extends the result of {\it R. L. Taylor} et al. [Stochastic Anal. Appl. 20, No. 3, 643--656 (2002; Zbl 1003.60032)] on unweighted averages to weighted averages.

62G05Nonparametric estimation
60F15Strong limit theorems
Full Text: DOI
[1] Amini M, Bozorgnia A (2000) Negatively dependent bounded random variable probability inequalities and the strong law of large numbers. J Appl Math Stoch Anal 13: 261--267 · Zbl 1070.60028 · doi:10.1155/S104895330000023X
[2] Amini M, Bozorgnia A (2003) Complete convergence for negatively dependent random variables. J Appl Math Stoch Anal 16: 121--126 · Zbl 1040.60021 · doi:10.1155/S104895330300008X
[3] Amini M, Azarnoosh HA, Bozorgnia A (2004) The strong law of large numbers for negatively dependent generalized Gaussian random variables. Stoch Anal Appl 22: 893--901 · Zbl 1056.60024 · doi:10.1081/SAP-120037623
[4] Amini M, Zarei H, Bozorgnia A (2007) Some strong limit theorems of weighted sums for negatively dependent generalized Gaussian random variables. Stat Probab Lett 77: 1106--1110 · Zbl 1120.60022 · doi:10.1016/j.spl.2007.01.015
[5] Asadian N, Fakoor V, Bozorgnia A (2006) Rosenthal’s type inequalities for negatively orthant dependent random variables. JIRSS 5: 69--75
[6] Chow YS (1966) Some convergence theorems for independent random variables. Ann Math Stat 37: 1482--1493 · Zbl 0152.16905 · doi:10.1214/aoms/1177699140
[7] Ebrahimi N, Ghosh M (1981) Multivariate negative dependence. Commun Stat Theory Methods A 10: 307--337 · Zbl 0506.62034 · doi:10.1080/03610928108828041
[8] Erdös P (1949) On a theorem of Hsu and Robbins. Ann Math Stat 20: 286--291 · Zbl 0033.29001 · doi:10.1214/aoms/1177730037
[9] 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
[10] 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
[11] Katz M (1963) The probability in the tail of a distribution. Ann Math Stat 34: 312--318 · Zbl 0209.49503 · doi:10.1214/aoms/1177704268
[12] Klesov O, Rosalsky A, Volodin AI (2005) On the almost sure growth rate of sums of lower negatively dependent nonnegative random variables. Stat Prob Lett 71: 193--202 · Zbl 1070.60030 · doi:10.1016/j.spl.2004.10.027
[13] Kuczmaszewska A (2006) On some conditions for complete convergence for arrays of rowwise negatively dependent random variables. Stoch Anal Appl 24: 1083--1095 · Zbl 1108.60021 · doi:10.1080/07362990600958754
[14] Lehmann EL (1966) Some concepts of dependence. Ann Math Stat 37: 1137--1153 · Zbl 0146.40601 · doi:10.1214/aoms/1177699260
[15] Li D, Rosalsky A, Volodin AI (2006) On the strong law of large numbers for sequences of pairwise negative quadrant dependent random variables. Bull Inst Math Acad Sin (N.S.) 1: 281--305 · Zbl 1102.60026
[16] Stout WF (1968) Some results on the complete and almost sure convergence of linear combinations of independent random variables and martingale differences. Ann Math Stat 39: 1549--1562 · Zbl 0165.52702
[17] Stout WF (1974) Almost sure convergence. Academic Press, New York · Zbl 0321.60022
[18] Taylor RL, Patterson RF, Bozorgnia A (2002) A strong law of large numbers for arrays of rowwise negatively dependent random variables. Stoch Anal Appl 20: 643--656 · Zbl 1003.60032 · doi:10.1081/SAP-120004118
[19] Volodin A (2002) On the Kolmogorov exponential inequality for negatively dependent random variables. Pak J Stat 18: 249--254 · Zbl 1128.60304
[20] Zarei H, Jabbari H (2009) Complete convergence of weighted sums under negative dependence. Stat Papers doi: 10.1007/s00362-009-0238-4 · Zbl 1247.60044