Geodesic
Lower bounds for average sample size in the tests of goodness-of-fit and homogeneity
Teoriâ veroâtnostej i ee primeneniâ, Tome 24 (1979) no. 3, pp. 637-645

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The problems of testing hypothesis $P=P_0$ on the distribution $P$ of random variable $\xi$ against the class of alternatives $$ \mathscr P_1=\{P\colon \sup_A|P(A)-P_0(A)|\ge\Delta\} $$ and of testing hypothesis $P_1=P_2$ on the distributions $P_1$ and $P_2$ of independent random variables $\xi$ and $\eta$ against the class of alternatives $$ \mathscr P_2=\{(P_1,P_2)\colon \sup_A|P_1(A)-P_2(A)|\ge\Delta\} $$ are considered. Lower bounds for average sample size which is sufficient for the acceptance of decision with guaranted restrictions $(\alpha,\beta)$ on the probabilities of errors are established. The asymptotical (for $\Delta\to 0$) efficiency of Kolmogorov and Smirnov tests with respect to obtained bounds is investigated. 
@article{TVP_1979_24_3_a22,
     author = {I. N. Volodin},
     title = {Lower bounds for average sample size in the tests of goodness-of-fit and homogeneity},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {637--645},
     publisher = {mathdoc},
     volume = {24},
     number = {3},
     year = {1979},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1979_24_3_a22/}
}
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I. N. Volodin. Lower bounds for average sample size in the tests of goodness-of-fit and homogeneity. Teoriâ veroâtnostej i ee primeneniâ, Tome 24 (1979) no. 3, pp. 637-645. http://geodesic.mathdoc.fr/item/TVP_1979_24_3_a22/