A Comparative Study of Ten Asymmetry Tests

Abstract

In this paper, we investigate the properties of some common tests for Asymmetry. The tests are based on Moments, Order Statistics and Empirical Characteristic Functions, respectively. These tests have completely different origins, rely on different characterizations of symmetry and have very different size and power properties. It is demonstrated that tests based on Empirical Characteristic Functions are strongly dependent on the choice of working region and that some previously proposed tests may be improved considerably by using Bootstrapped critical values. It is also concluded that no test is uniformly better than the others but that the Empirical Characteristic Function tests have best over-all properties.