ALMOST SURE CONVERGENCE FOR WEIGHTED SUMS OF NEGATIVELY ORTHANT DEPENDENT RANDOM VARIABLES

Title & Authors
ALMOST SURE CONVERGENCE FOR WEIGHTED SUMS OF NEGATIVELY ORTHANT DEPENDENT RANDOM VARIABLES
Ko, MI-HwA; KIM, TAE-SUNG;

Abstract
For weighted sum of a sequence {X, X$\small{\_{n}}$, n $\small{\geq}$ 1} of identically distributed, negatively orthant dependent random variables such that |r| > 0, has a finite moment generating function, a strong law of large numbers is established.
Keywords
negatively orthant dependent random variables;strong law of large numbers;identically distributed;moment generating function;weighted sum;
Language
English
Cited by
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References
1.
Z. D. Bai and P. E. Cheng, Marcinkiewicz strong laws for linear statistics, Statist. Probab. Lett. 46 (2000), 105-112

2.
T. K. Chandra and S. Ghosal, Extensions of the strong law of large numbers of Marcinkiewicz and Zygmund for dependent random variables, Acta. Math. Hun- gar. 71 (1996), 327-336

3.
R. Cheng and S. Gan, Almost sure convergence of weighted sums of NA sequences, Wuhan Univ. J. Nat. Sci. 3 (1998), 11-16

4.
Y. S. Chow and T. L. Lai, Limiting behavior of weighted sums of independent random variables, Ann. Probab. 1 (1973), 810-824

5.
J. Cuzick, A strong law for weighted sums of i.i.d. random variables, J. Theoret. Probab. 8 (1995), 625-641

6.
N. Ebrahimi and M. Ghosh, Multivariate Negative Dependence, Comm. Statist. Theory Methods 10 (1981), 307-336

7.
E. L. Lehmann, Some Concepts of Dependence, Ann. Statist. 43 (1966), 1137- 1153

8.
P. Matula, A note on the almost sure convergence of sums of negatively dependent random variables, Statist. Probab. Lett. 15 (1992), 209-213

9.
Y. Qi, Limit theorems for sums and maxima of pairwise negative quadrant depen- dent random variables Syst. Sci. Math. Sci. 8 (1995), 251-253

10.
W. F. Stout, Almost Sure Convergence, Academic Press, New York, 1974

11.
H. Teicher, Almost certain convergence in double arrays, Z. Wahrsch. Verw. Gebiete 69 (1985), 331-345