Vanishing Shortcoming and Asymptotic Relative Efficiency

摘要

The shortcoming of a test is the difference between the maximal attainable power211u001eand the power of the test under consideration. Vanishing shortcoming, when the 211u001enumber of observations tends to infinity, is therefore an optimality property of 211u001ea test. Other familiar optimality criteria are based on the asymptotic relative 211u001eefficiency of the test. The relations between these optimality criteria are 211u001einvestigated. It turns out that vanishing shortcoming is seemingly slightly 211u001estronger than first order efficiency, but in regular cases there is equivalence. 211u001eThe results are in particular applied on tests for goodness-of-fit.