Testing Axial Symmetry by Means of Directional Quantile Regression Coefficients

Testing axial symmetry given the axial direction has recently attracted considerable attention not only because of its direct practical applications but also because of its wide implications for testing exchangeability, independence, goodness-of-fit, or equality of scale. The contribution extends the family of recently developed tests of axial symmetry with new members that are based on coefficient estimates in directional quantile regression. The proposed testing tools are especially suitable for the situations not covered well by available competitors, i.e., in the linear regression context or when regression rank scores are not available. The performance of the new tests in such settings is illustrated with a few representative simulation experiments.