Geodesic
Asymptotic minimaxity of tests of the Kolmogorov and omega-square types
Teoriâ veroâtnostej i ee primeneniâ, Tome 40 (1995) no. 1, pp. 54-67

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The asymptotic minimaxity of tests of the Kolmogorov and omega-square types is proved under natural nonparametric sets of alternatives. The tests are compared using a new asymptotic bound for the probabilities of moderate large deviations for the type I and type II errors. Our proof relies heavily on qualitatively new theorems about the probabilities of moderate large deviations of empirical measures.
Keywords: nonparametric hypotheses testing, asymptotic efficiency, asymptotic minimaxity, large deviations, Kolmogorov's test, omega-square test. 
@article{TVP_1995_40_1_a1,
     author = {M. S. Ermakov},
     title = {Asymptotic minimaxity of tests of the {Kolmogorov} and omega-square types},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {54--67},
     publisher = {mathdoc},
     volume = {40},
     number = {1},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1995_40_1_a1/}
}
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M. S. Ermakov. Asymptotic minimaxity of tests of the Kolmogorov and omega-square types. Teoriâ veroâtnostej i ee primeneniâ, Tome 40 (1995) no. 1, pp. 54-67. http://geodesic.mathdoc.fr/item/TVP_1995_40_1_a1/