Tests for Symmetry of Regression Errors

In this essay we discuss how to test for symmetry of unobservable errors. Two easily computable test statistics based on the estimated regression residuals are developed. Alternatively, we consider various nonparametric procedures that have been proposed in the literature to test for symmetry of observations; they can be used in this framework replacing the unknown errors by well-behaved residuals. Monte Carlo experiments show that for the cases investigated, the tests under consideration have reasonably good size and power performance in small samples when critical values are obtained using a boostrap procedure. We also establish consistency property of the bootstrap.