摘要：The article describes how directional quantiles can be useful for testing the null hypothesis that a multivariate distribution is symmetric around a line in a given direction. It also generalizes the proposed tests to residual distributions in a linear regression setup, discusses their use for statistical inference regarding equality of distributions, equality of scale, or exchangeability, and illustrates the achievements with carefully designed pictures and examples.
关键词：62H15; 62J99; Axial symmetry; directional quantile; exchangeability; permutation symmetry; Quantile regression; symmetry around a line
