On large deviations of type II error probabilities of Kolmogorov and omega-squared tests

For the Kolmogorov and omega-squred tests the strong asymptotics for large deviations of type II error probabilities are obtained in the case of “least favourable alternatives.” Using these asymptotics the type II error probabilities for any sequence of alternatives can be easily estimated. The proofs are based on one exact asymptotics for large deviation probabilities for Gaussian measures in the Hilbert space and a theorem on large deviation probabilities of sums of independent random vectors in Banach space (see [12]).