Normality Tests with Robust Scale Estimators

The well known Jarque-Bera (JB) test for normality uses the sample mean and sample standard deviation for estimating the population mean and population standard deviation. Instead of the sample standard deviation, Gel and Gastwirth (2008) proposed to use a robust scale estimator, known as the “average absolute deviation from the median”, in constructing the JB test statistic. The resulting test, which is called the “robust JB test”, performs better than the usual JB test against symmetric fat-tailed distributions in small samples. In this paper, we examine the usage of other robust scale estimators. Our simulation study demonstrates that one of our newly proposed normality tests has the power comparable to the robust JB test against symmetric fat-tailed distributions, and is much more powerful than the robust JB test against asymmetric distributions