Geodesic
Decomposable statistics and hypothesis testing. The case of small samples
Teoriâ veroâtnostej i ee primeneniâ, Tome 23 (1978) no. 4, pp. 796-806

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Questions of statistical hypotheses testing are considered for polynomial outcome probabilities in the scheme of series under the conditions that the number of outcomes $N$ and the number of tests $n$ increase simultaneously to infinity so that $n/N$ remains bounded. A class of tests is studied which is based on decomposable statistics of outcomes, frequencies. In particular, some results are obtained concerning the classical $\chi^2$-test and maximum likelihood ratio test. 
@article{TVP_1978_23_4_a7,
     author = {G. I. Iv\v{c}enko and Yu. I. Medvedev},
     title = {Decomposable statistics and hypothesis testing. {The} case of small samples},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {796--806},
     publisher = {mathdoc},
     volume = {23},
     number = {4},
     year = {1978},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1978_23_4_a7/}
}
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G. I. Ivčenko; Yu. I. Medvedev. Decomposable statistics and hypothesis testing. The case of small samples. Teoriâ veroâtnostej i ee primeneniâ, Tome 23 (1978) no. 4, pp. 796-806. http://geodesic.mathdoc.fr/item/TVP_1978_23_4_a7/