Local exact Bahadur efficiencies of two scale-free tests of normality based on a recent characterization

We consider two scale-free tests of normality based on the characterization of the symmetric normal law by Ahsanullah et al. (Normal and student’s t-distributions and their applications, Springer, Berlin, 2014). Both tests have an U-empirical structure, but the first one is of integral type, while the second one is of Kolmogorov type. We discuss the limiting behavior of the test statistics and calculate their local exact Bahadur efficiency for location, skew and contamination alternatives.