Geodesic
On inequalities for large deviations of certain statistics
Teoriâ veroâtnostej i ee primeneniâ, Tome 16 (1971) no. 2, pp. 386-389

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This paper deals with multidimensional variants of the Kolmogorov–Smirnov and $\omega^2$-tests. In section 1, exponentially decreasing bounds are given for the first kind error probability. In section 2, rough estimates are derived for the power of the tests under consideration. 
@article{TVP_1971_16_2_a18,
     author = {V. V. Yurinskiǐ},
     title = {On inequalities for large deviations of certain statistics},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {386--389},
     publisher = {mathdoc},
     volume = {16},
     number = {2},
     year = {1971},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1971_16_2_a18/}
}
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V. V. Yurinskiǐ. On inequalities for large deviations of certain statistics. Teoriâ veroâtnostej i ee primeneniâ, Tome 16 (1971) no. 2, pp. 386-389. http://geodesic.mathdoc.fr/item/TVP_1971_16_2_a18/