A modification of the Jarque-Bera test for normality

Abstract

In regression analysis, many statistical tests have been proposed to find out whether the error term is normally distributed or not. These statistical tests are typically constructed using OLS residuals. However, since diagnostic tests for normality are very sensitive to outliers, they have a zero breakdown value. In this paper, we attempt to investigate the effects of using residuals from robust regression replacing OLS residuals in test statistics for normality. We study a modified Jarque-Bera test statistic for normality based on robust regression residuals. The asymptotic distribution of this robustified normality test is derived, and its breakdown property is discussed.