A normality test for the errors of the linear model

We present a normality test for the errors of the linear regression model based on the normality test in Epps and Pulley (1983). We prove that the presented test is consistent against any alternative. We show that the test statistic under the null hypothesis is asympotically equivalent to a degenerate V-statistic. We also consider the asymptotic distribution of the test under contiguous alternatives.