Geodesic
A uniqueness property of the chi-square distribution
Teoriâ veroâtnostej i ee primeneniâ, Tome 40 (1995) no. 1, pp. 159-165

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We show conditions under which the chi-square statistic in the polynomial scheme is (up to a functional transformation) a unique statistic whose asymptotic distribution (when the number of observations grows to infinity) depends only on a one-dimensional parameter on the set of contiguous alternatives.
Keywords: chi-square statistic, nuisance parameters, uniqueness. 
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     author = {N. K. Bakirov},
     title = {A uniqueness property of the chi-square distribution},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {159--165},
     publisher = {mathdoc},
     volume = {40},
     number = {1},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1995_40_1_a8/}
}
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N. K. Bakirov. A uniqueness property of the chi-square distribution. Teoriâ veroâtnostej i ee primeneniâ, Tome 40 (1995) no. 1, pp. 159-165. http://geodesic.mathdoc.fr/item/TVP_1995_40_1_a8/