Geodesic
Large deviations for empirical probability measures and statistical tests
Zapiski Nauchnykh Seminarov POMI, Studies in mathematical statistics. Part 10, Tome 207 (1993), pp. 37-59

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Given subsets $\Omega,\Phi$ of a set of probability measures, questions about the uniform in $P\in\Phi$ convergence of the normalized large deviations $n^{-1}\log P$ ($\hat P_n\in\Omega$) and about the convergence of the supremum over $\Phi$ of this value are considered for empirical distributions $\hat P_n$. The results are used for the proof of the asymptotic minimaxity of the Kolmogorov, omega-square, and rank tests by nonparametric sets of alternatives. A new bound for the efficiency of statistical tests is obtained. Bibliography: 19 titles. 
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     author = {M. S. Ermakov},
     title = {Large deviations for empirical probability measures and statistical tests},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {37--59},
     publisher = {mathdoc},
     volume = {207},
     year = {1993},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1993_207_a3/}
}
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M. S. Ermakov. Large deviations for empirical probability measures and statistical tests. Zapiski Nauchnykh Seminarov POMI, Studies in mathematical statistics. Part 10, Tome 207 (1993), pp. 37-59. http://geodesic.mathdoc.fr/item/ZNSL_1993_207_a3/