Линьков Ю. Н.

We consider the problem of testing of a finite number of simple hypotheses in general scheme of statistical experiments. Under condition of the validity of theorems on large deviations for logarithm of likelihood ratio, we investigate the asymptotic behavior of probabilities of errors of the Bayes criterion. We obtain asymptotics of the Shannon information containing in an observation and in the Bayes criterion.

The general limit theorem on probability of large deviations of the logarithm of the likelihood ratio under the null hypothesis and under alternative is proved. Weaker versions of the theorem on large deviations are obtained in predictable terms for the problem of distinguishing counting processes. The case of counting processes with deterministic compensators is investigated.

A canonical representation foi the logarithm of the likelihood ratio and limit theorems on its asymptotic behavior are obtained. By using these theorems, the rate of decrease of probability of the second type error in the Neyman - Pearson test is studied.