Testing bivariate symmetry

Abstract

We consider the most basic concept of bivariate symmetry, referred to as general symmetry or conditional symmetry and provide a necessary condition for it based on the joint probability density function and the associated cumulative distribution function. This condition is then used to provide a test of general bivariate symmetry by using the sample analog of the necessary condition as a test statistic. We derive the asymptotic distribution of the test statistic under the null hypothesis and exhibit the performance of the proposed test through simulations. The test is then applied to a couple of real datasets, one coming from an insurance company and the other from a medical trial of Mayo Clinic.