Mathematical Statistics and Limit Theorems. Festschrift in Honour of Paul Deheuvels. M. Hallin, D. Mason, D. Pfeifer, J. Steinebach (Eds.)
We use the characterization of distribution symmetry in terms of order statistics in order to obtain new tests of symmetry based on U-empirical distribution functions. We calculate their limiting distributions and large deviations and explore their local Bahadur efficiency against location alternatives which turns out to be rather high.
We use a characterization of symmetry via order statistics to establish two new tests of symmetry which have U-empirical nature.
Limiting distributions and large deviations of new statistics are found, and local Bahadur efficiency is calculated.