Geodesic
Decomposable statistics and the hypotheses testing for groupped data
Teoriâ veroâtnostej i ee primeneniâ, Tome 25 (1980) no. 3, pp. 549-560 
G. I. Ivčenko; Yu. I. Medvedev. Decomposable statistics and the hypotheses testing for groupped data. Teoriâ veroâtnostej i ee primeneniâ, Tome 25 (1980) no. 3, pp. 549-560. http://geodesic.mathdoc.fr/item/TVP_1980_25_3_a8/
@article{TVP_1980_25_3_a8,
     author = {G. I. Iv\v{c}enko and Yu. I. Medvedev},
     title = {Decomposable statistics and the hypotheses testing for groupped data},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {549--560},
     year = {1980},
     volume = {25},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1980_25_3_a8/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The paper deals with testing a simple hypothesis against alternatives converging to the hypothesis at rate $n^{-1/2}$ ($n$ being the sample size) in the case when the number of classes-intervals increases infinitely together with $n$. The concept of highly sensitive criterion is introduced and general features of such criteria generated by decomposable statistics ([2]) are studied. It is shown that in the class of criteria under consideration the optimal (in a some sense) criteria are linear criteria, each of them being the most powerful test.