Geodesic
On the absolute significance test for polynomial distribution
Teoriâ veroâtnostej i ee primeneniâ, Tome 42 (1997) no. 4, pp. 731-746 Cet article a éte moissonné depuis la source Math-Net.Ru

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Upper estimates are found for the sum of probabilities of all the events $(x_1\ldots x_r)$, where $x_k$ is the frequency of the $k$th outcome in $n$ independent trials carried out according to a polynomial scheme of trials with $r$ possible outcomes, the probability of each of which does not exceed the probability of a fixed event observed in $n$ independent trials carried out according to the same scheme. Using these estimates we construct a test rejecting a polynomial scheme when the probabilities of outcomes in it are known.
Keywords: polynomial scheme of trials, absolute significance test, Kullback–Leibler distance, consistency of a test under a simple alternative, convex programming. 
@article{TVP_1997_42_4_a4,
     author = {N. P. Salikhov},
     title = {On the absolute significance test for~polynomial distribution},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {731--746},
     year = {1997},
     volume = {42},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1997_42_4_a4/}
}
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N. P. Salikhov. On the absolute significance test for polynomial distribution. Teoriâ veroâtnostej i ee primeneniâ, Tome 42 (1997) no. 4, pp. 731-746. http://geodesic.mathdoc.fr/item/TVP_1997_42_4_a4/