Testing for elliptical symmetry of errors in the multivariate linear regression model

摘要

This paper presents a characteristic test for testing the elliptical distribution of the errors in the multivariate linear regression model. We obtain the asymptotic spherical distribution of the transformed residuals of the regression model under the null hypothesis. Based on bootstrap approximation, an algorithm is given to estimate the critical values of the test. The test statistic possesses symmetry and then the test power can be enhanced. The test is practical to implement for arbitrary dimension of the errors.