Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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ON THE STRONG LAW OF LARGE NUMBERS FOR WEIGHTED SUMS OF ARRAYS OF ROWWISE NEGATIVELY DEPENDENT RANDOM VARIABLES

  • Baek, Jong-Il (SCHOOL OF MATHEMATICS AND INFORMATIONAL STATISTICS AND BASIC NATURAL SCIENCE WONKWANG UNIVERSITY) ;
  • Seo, Hye-Young (SCHOOL OF MATHEMATICS AND INFORMATIONAL STATISTICS AND BASIC NATURAL SCIENCE WONKWANG UNIVERSITY) ;
  • Lee, Gil-Hwan (SCHOOL OF MATHEMATICS AND INFORMATIONAL STATISTICS AND BASIC NATURAL SCIENCE WONKWANG UNIVERSITY) ;
  • Choi, Jeong-Yeol (SCHOOL OF MATHEMATICS AND INFORMATIONAL STATISTICS AND BASIC NATURAL SCIENCE WONKWANG UNIVERSITY)
  • Published : 2009.07.01
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Abstract

Let {$X_{ni}$ | $1{\leq}i{\leq}n,\;n{\geq}1$} be an array of rowwise negatively dependent (ND) random variables. We in this paper discuss the conditions of ${\sum}^n_{t=1}a_{ni}X_{ni}{\rightarrow}0$ completely as $n{\rightarrow}{\infty}$ under not necessarily identically distributed setting and the strong law of large numbers for weighted sums of arrays of rowwise negatively dependent random variables is also considered.

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References

  1. A. Bozorgnia, R. F. Patterson, and R. L. Taylor, Limit theorems for dependent random variables, World Congress of Nonlinear Analysts '92, Vol. I–IV (Tampa, FL, 1992), 1639–1650, de Gruyter, Berlin, 1996
  2. N. Ebrahimi and M. Ghosh, Multivariate negative dependence, Comm. Statist. A-Theory Methods 10 (1981), no. 4, 307–337 https://doi.org/10.1080/03610928108828041
  3. P. Erdos, On a theorem of Hsu and Robbins, Ann. Math. Statistics 20 (1949), 286–291 https://doi.org/10.1214/aoms/1177730037
  4. P. L. Hsu and H. Robbins, Complete convergence and the law of large numbers, Proc. Nat. Acad. Sci. U. S. A. 33 (1947), 25–31 https://doi.org/10.1073/pnas.33.2.25
  5. T. C. Hu, F. Moricz, and R. L. Taylor, Strong laws of large numbers for arrays of rowwise independent random variables, Acta Math. Hungar. 54 (1989), no. 1-2, 153–162 https://doi.org/10.1007/BF01950716
  6. T. C. Hu, F. Moricz, and R. L. Taylor, Strong laws of large numbers for arrays of rowwise independent random variables, Statistics Technical Report 27 (1986), University of Georgia https://doi.org/10.1007/BF01950716
  7. R. L. Taylor and T. C. Hu, Sub-Gaussian techniques in proving strong laws of large numbers, Amer. Math. Monthly 94 (1987), no. 3, 295–299 https://doi.org/10.2307/2323401
  8. R. L. Taylor, R. F. Patterson, and A. Bozorgnia, A strong law of large numbers for arrays of rowwise negatively dependent random variables, Stochastic Anal. Appl. 20 (2002), no. 3, 643–656 https://doi.org/10.1081/SAP-120004118

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