Abstract: We propose a modification of the data driven score rank tests studied recently in Inglot et al. (2012) by an appropriate choice of the orthonormal system. The simulation study confirms much better performance of the new tests for alternatives with dominating asymmetry in the tails and comparable sensitivity for other types of alternatives. In effect we obtain omnibus tests for symmetry which are equal to the best existing procedures for typical alternatives and overtake them significantly for atypical ones.

2000 AMS Mathematics Subject Classification: Primary: 62G10; Secondary: 62G30, 65C05, 65C60.

Keywords and phrases: Testing symmetry, non-smooth functions, data driven score test, effective score, Schwarz-type rule, model selection, rank test, Monte Carlo study.