Open Access
2021 Testing axial symmetry by means of directional regression quantiles
Šárka Hudecová, Miroslav Šiman
Author Affiliations +
Electron. J. Statist. 15(1): 2690-2715 (2021). DOI: 10.1214/21-EJS1850


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.


The authors would like to thank anonymous referees for valuable comments and suggestions.


Download Citation

Šárka Hudecová. Miroslav Šiman. "Testing axial symmetry by means of directional regression quantiles." Electron. J. Statist. 15 (1) 2690 - 2715, 2021.


Received: 1 January 2021; Published: 2021
First available in Project Euclid: 12 May 2021

Digital Object Identifier: 10.1214/21-EJS1850

Primary: 62H15
Secondary: 62J99

Keywords: Axial symmetry , directional quantile , exchangeability , permutation symmetry , Quantile regression , symmetry around a line

Vol.15 • No. 1 • 2021
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