Geodesic
Conditions for the asymptotic normality of multidimensional randomized decomposable statistics
Diskretnaya Matematika, Tome 1 (1989) no. 2, pp. 219-227.

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A theorem on asymptotic normality of multidimensional randomized decomposable statistics is proved. The conditions of the theorem are weaker than the known restrictions on the parameters of a polynomial distribution and on functions, which generate decomposable statistics. 
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     author = {S. I. Bykov and V. A. Ivanov},
     title = {Conditions for the asymptotic normality of multidimensional randomized decomposable statistics},
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S. I. Bykov; V. A. Ivanov. Conditions for the asymptotic normality of multidimensional randomized decomposable statistics. Diskretnaya Matematika, Tome 1 (1989) no. 2, pp. 219-227. http://geodesic.mathdoc.fr/item/DM_1989_1_2_a5/