Geodesic
Decomposable statistics in a polynomial scheme.~II
Teoriâ veroâtnostej i ee primeneniâ, Tome 22 (1977) no. 3, pp. 623-631

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Let a random vector $\nu=(\nu_1,\dots,\nu_N)$ be polynomially distributed with parameters $n;p_1,\dots,p_N$. The paper deals with limiting laws of the statistic $\chi^2$, maximum likelihood ratio, linear combinations of random variables $\mu_r$, where $\mu_r$ is the number of coordinates of $\nu$ equal to $r$. The scheme of series is considered, the number of outcomes $N$ and the number of tests $n$ increasing simultaneously to infinity so that $n/N=O(1)$. 
@article{TVP_1977_22_3_a18,
     author = {Yu. I. Medvedev},
     title = {Decomposable statistics in a polynomial {scheme.~II}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {623--631},
     publisher = {mathdoc},
     volume = {22},
     number = {3},
     year = {1977},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1977_22_3_a18/}
}
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Yu. I. Medvedev. Decomposable statistics in a polynomial scheme.~II. Teoriâ veroâtnostej i ee primeneniâ, Tome 22 (1977) no. 3, pp. 623-631. http://geodesic.mathdoc.fr/item/TVP_1977_22_3_a18/