A bootstrap test for symmetry based on quantiles

Abstract

In this paper, we construct a nonparametric test for the symmetry assumption of an underling distribution based on the sample quantiles. Bootstrap re-sampling from a symmetric empirical distribution function is used to obtain the p-value of the test. The power of the new test statistic is compared with some well-known symmetry tests using a simulation study. The results show that the proposed test preserves its level and it has reasonable power properties on the family of distribution evaluated.