Probabilities of Large Deviations of Type II Errors for Tests of Kolmogorov and Omega-Square Types

Research paper by M. S. Ermakov

Indexed on: 01 Jul '05Published on: 01 Jul '05Published in: Journal of Mathematical Sciences


For the Kolmogorov and omega-square tests, strong asymptotics for large deviations of type II error probabilities are obtained in the case of “least favorable alternatives.” Using these asymptotics, type II error probabilities for any sequence of alternatives can readily be estimated. The proofs are based on an exact asymptotic of large deviation probabilities for Gaussian measures in a Hilbert space and on a theorem on large deviation probabilities for sums of independent random vectors in a Banach space. Bibliography: 22 titles.