A method for resolving ties in asymptotic relative efficiency

This article presents a method for determining which of two tests may offer an advantage in power when their asymptotic relative efficiencies (ARE) are the same. The method maintains some of the desirable properties of ARE, such as ease of calculation and singular result based upon asymptotic properties of the tests. However, using higher-order Taylor expansions of the test statistics’ means, the procedure offers additional insight into the finite sample size behavior of the tests. Two examples demonstrate the method.