Refi ned data driven tests for univariate symmetry
Słowa kluczowe:Testing symmetry, non-smooth functions, data driven score test, effective score, Schwarz-type rule, model selection, rank test, Monte Carlo study
We propose a modification of the data driven score rank tests studied recently in Inglot et al. 2012 by an appropriate choice of the orthonormalsystem. The simulation study confirms much better performanceof the new tests for alternatives with dominating asymmetry in the tails andcomparable sensitivity for other types of alternatives. In effect we obtainomnibus tests for symmetry which are equal to the best existing proceduresfor typical alternatives and overtake them significantly for atypical ones.