1. Institute of Mathematics and Informatics, Wroc?aw University of Technology, Wybrze?e Wyspiańskiego 27, 50-370 Wroc?aw, Poland;2. Institute of Mathematics, Polish Academy of Sciences, ul. Kopernika 18, 51-617 Wroc?aw, Poland
Abstract:
We study a modification of the notion of asymptotic intermediate efficiency of statistical tests by defining it in terms of shifting alternatives. We prove a theorem providing conditions for its existence and show that this modification is closely related to the original Kallenberg's asymptotic intermediate efficiency in a quite general setting. Next, we find estimates for differences between powers of the Neyman–Pearson test under original alternatives and that of a given test under shifted alternatives. We also present some simulation results. They attest to consistency of theoretical results with observed empirical powers for quite small sample sizes.