New integral nonparametric test for the hypothesis of affine symmetry

The hypothesis of affine symmetry introduced by P. K. Sen in 1978 consists in the symmetry about the origin and in the same time in the independence of the components of two-dimensional random vector. New test statistic for testing this hypothesis is proposed. Some asymptotic properties of this statistic are investigated, in particular limiting distribution and large deviations. Bahadur local efficiency is also found and analyzed. Bibl. 18 titles.