Testing Symmetry of the Errors of a Linear Model

A test for symmetry of the distribution of the errors in a linear model is proposed. It is a goodness-of-fit type test based on the discrepancy between two robust fits. The first fit is appropriate under symmetric errors while the second is appropriate for skewed as well as symmetric distributions. The proposed test is robust and is asymptotically distribution free. Besides deriving the test statistic’s null asymptotic distribution, its efficiency under a general class of local alternative is obtained which allows for the determination of the test’s asymptotic relative efficiency with its competitors.