Notes on robustness of RT class tests for normality

The assumption of normal distribution of a random variable plays an important role in various fields of science. The Jarque-Bera test is the most widely adopted omnibus test of normality in econometrics, finance and related fields. As outliers in the data sets in the field of economics and finance are frequently present, the Jarque-Bera test is not sufficiently robust, since it is based on the classical characteristics of skewness and kurtosis and has a zero breakdown value. Thus, the Jarque-Bera test is very sensitive to small deviations from normality, e.g. presence of outliers. In this contribution, we introduce the general RT class of robust tests for normality which is less sensitive to small deviations from normality, particularly in the form of a few outliers. We also present and discuss the trade-off between power and robustness of selected classical and robust normality tests of random variables where outliers could be presented.