Geodesic
Convergence of one partial form of sums of dependent random vectors to a~normal distribution
Matematičeskie zametki, Tome 5 (1969) no. 6, pp. 691-695.

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The method of moments is used to establish an asymptotic normal distribution for a sequence of dependent random vectors of special form. 
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L. A. Zolotuhina; K. P. Latishev; V. N. Chugueva. Convergence of one partial form of sums of dependent random vectors to a~normal distribution. Matematičeskie zametki, Tome 5 (1969) no. 6, pp. 691-695. http://geodesic.mathdoc.fr/item/MZM_1969_5_6_a5/