New $U$-empirical tests of symmetry based on extremal order statistics,   and their efficiencies
  We use a characterization of symmetry in terms of extremal order statistics which enables to build several new nonparametric tests of symmetry. We discuss their limiting distributions and calculate their local exact Bahadur efficiency under location alternative which is mostly high. 
Ya. Yu. Nikitin, M. Ahsanullah
math.ST stat.TH