The performance of univariate goodness-of-fit tests for normality based on the empirical characteristic function in large samples

摘要

A test based on the studentized empirical characteristic function calculated in a single point is derived. An empirical power comparison is made between this test and tests like the Epps-Pulley, Shapiro-Wilks, Anderson-Darling and other tests for normality. It is shown to outperform the more complicated Epps-Pulley test based on the empirical characteristic function and a Cramer-von Mises type expression in a simulation study. The test performs especially good in large samples and the derived test statistic has an asymptotic normal distribution which is easy to apply.