Omnibus tests for the error distribution in the linear regression model

Abstract

Test procedures are constructed for testing the goodness-of-fit of the error distribution in the regression context. The test statistic is based on an L 2-type distance between the characteristic function of the (assumed) error distribution and the empirical characteristic function of the residuals. The asymptotic null distribution as well as the behavior of the test statistic under contiguous alternatives is investigated, while the issue of the choice of suitable estimators has been particularly emphasized. Theoretical results are accompanied by a simulation study.