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).skew family; linear rank test; Maesono statistic; Bahadur efficiency; local optimality

Local asympotic efficiency of some goodness-of-fit tests under skew alternatives.

The efficiency of most known distribution-free goodness-of-fitt tests such as Kolmogorov - Smirnov, Cramér - von Mises and their numerous variants was studied mainly under the classical alternatives of location and scale. However it is interesting to compare the efficiencies of these tests under asymmetric alternatives among which the most popular is the so-called skew alternative proposed by Azzalini (1985) in the case of the normal distribution. We find and compare local Bahadur efficiencies of many known statistics for skew alternatives and discuss also the conditions of their local optimality.Bahadur efficiency; skew alternative; local index; Kullback-Leibler information; local asymptotic optimality; arcsine density