Asympotic efficiency of signed - rank symmetry tests under skew alternatives.

The efficiency of some known tests for symmetry such as the sign test, the Wilcoxon signed-rank test or more general linear signed rank tests was studied mainly under the classical alternatives of location. However it is interesting to compare the efficiencies of these tests under asymmetric alternatives like the so-called skew alternative proposed in Azzalini (1985). We find and compare local Bahadur efficiencies of linear signed-rank statistics for skew alternatives and discuss also the conditions of their local optimality. We calculate also such efficiencies for the family of distribution-free Maesono statistics proposed in Maesono (1987).