Large deviation theorems in the problem of testing two simple hypotheses

Limit theorems on large deviations of the logarithm of the likelihood ratio are proved for the problem of distinguishing two simple hypotheses in the general scheme of statistical experiments under the null hypothesis and under an alternative hypothesis. The theorems obtained are applied to the investigation of a decrease in the probability of errors of the first and second kind for the Neumann-Pearson criterion.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 2, pp. 227–235, February, 1995.