Testing axial symmetry by means of directional regression quantiles

Abstract

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.

Keywords

• Axial symmetry
• exchangeability
• permutation symmetry
• symmetry around a line
• directional quantile
• quantile regression