논문KCI 등재
On the strong law of large numbers for weighted sums of arrays of rowwise negatively dependent random variables
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Let {X_{ni}|1≤ i≤ n,n≥1} be an array of rowwise negatively dependent (ND) random variables. We in this paper discuss the conditions of <수식> completely as n→∞ 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.
Abstract
Let {X_{ni}|1≤ i≤ n,n≥1} be an array of rowwise negatively dependent (ND) random variables. We in this paper discuss the conditions of <수식> completely as n→∞ 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.
참고문헌 (8)
- A. Bozorgnia, "Limit theorems for dependent random variables, World Congress of Nonlinear Analysts ’92", pp.1639~1650 (1996), de Gruyter
- N. Ebrahimi, "Multivariate negative dependence", Comm. Statist. A—Theory Methods, 10(4), pp.307~337 (1981)
- P. Erd¨os, "On a theorem of Hsu and Robbins", Ann. Math. Statistics, 20, pp.286~291 (1949)
- P. L. Hsu, "Complete convergence and the law of large numbers", Proc. Nat. Acad. Sci. U. S. A., 33, pp.25~31 (1947)
- T. C. Hu, "Strong laws of large numbers for arrays of rowwise independent random variables", Acta Math. Hungar., 54(1), pp.153~162 (1989)
- T. C. Hu, "Strong laws of large numbers for arrays of rowwise independent random variables", Statistics Technical Report, ~ (1986)
- R. L. Taylor, "Sub-Gaussian techniques in proving strong laws of large numbers", Amer. Math. Monthly, 94(3), pp.295~299 (1987)
- R. L. Taylor, "A strong law of large numbers for arrays of rowwise negatively dependent random variables", Stochastic Anal. Appl., 20(3), pp.643~656 (2002)
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