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.
Funding Statement
The research of Miroslav Šiman was supported by the Czech Science Foundation projects GA17-07384S and GA21-05325S. The research of Šárka Hudecová was supported by the Czech Science Foundation project GA18-08888S.
Acknowledgments
The authors would like to thank anonymous referees for valuable comments and suggestions.
Citation
Šárka Hudecová. Miroslav Šiman. "Testing axial symmetry by means of directional regression quantiles." Electron. J. Statist. 15 (1) 2690 - 2715, 2021. https://doi.org/10.1214/21-EJS1850
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