Bahadur efficiencies of the Epps–Pulley test for normality

The test for normality suggested by Epps and Pulley [9] is a serious competitor to tests based on the empirical distribution function. In contrast to the latter procedures, it has been generalized to obtain a genuine affine invariant and universally consistent test for normality in any dimension. We obtain approximate Bahadur efficiencies for the test of Epps and Pulley, thus complementing recent results of Milos̆ević et al. (see [15]). For certain values of a tuning parameter that is inherent in the Epps–Pulley test, this test outperforms each of its competitors considered in [15], over the whole range of six close alternatives to normality.