ASYMPTOTICAL QUESTIONS OF SIMPLE HYPOTHESES TESTING
Abstract: In this paper we consider the problem of the asymptotical behaviour of a power of
the Neyman-Pearson test with level as under different behaviour of
This problem is investigated for different types of an asymptotical distinguishability of
families of hypotheses and, in particular, for completely asymptotically distinguishable
families and contigual families. In the case of completely asymptotically distinguishable
families the rate of convergence to zero for the probability of the 2nd type errors is
investigated. In the case of contigual families the behaviour of is also studied when
the distribution of the logarithm of the likelihood ratio converges weakly to the distribution
which is not normal in general. At first these problems are considered in a general scheme of
statistical experiments, and then in the schemes generated by semimartingales.
2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;
Key words and phrases: -