Geodesic
Asymptotic normality of one class of statistics in a~multinomial scheme
Teoriâ veroâtnostej i ee primeneniâ, Tome 21 (1976) no. 1, pp. 190-195

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There are $N$ cells into which $n_j$ particles of the $j$-th type are thrown independently of each other, $j=1,\dots,s$. Particles of the $j$-th type are distributed in cells with the probabilities $p_{1j},\dots,p_{Nj}$. Let $$ L_r=\sum_{m=1}^N f_{mr}^{(N)}(\nu_{m1},\dots,\nu_{ms}), $$ where $\nu_{mj}$ is the number of particles of the $j$-th type in the $m$-th cell and $f_{mr}^{(N)}(x_1,\dots,x_s)$ are some given functions. The central limit theorem for the multidimensional random variables $(L_1,\dots,L_k)$, as $N,n_1,\dots,n_s\to\infty$, is proved. 
@article{TVP_1976_21_1_a20,
     author = {G. I. Iv\v{c}enko and V. V. Levin},
     title = {Asymptotic normality of one class of statistics in a~multinomial scheme},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {190--195},
     publisher = {mathdoc},
     volume = {21},
     number = {1},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1976_21_1_a20/}
}
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G. I. Ivčenko; V. V. Levin. Asymptotic normality of one class of statistics in a~multinomial scheme. Teoriâ veroâtnostej i ee primeneniâ, Tome 21 (1976) no. 1, pp. 190-195. http://geodesic.mathdoc.fr/item/TVP_1976_21_1_a20/