Testing axial symmetry by means of integrated rank scores

Abstrakt

The article addresses the recently emerging inferential problem of testing axial symmetry up to a shift, which is useful even for testing certain hypotheses of exchangeability, independence, goodness-of-fit or equality of scale. In particular, it introduces a new test of axial symmetry based on integrated rank scores for directional quantile regression.

The test outperforms existing competitors in terms of size, power, robustness, moment conditions or computational feasibility. All that is illustrated with a series of simulated examples.

Klíčová slova

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