  This paper investigates improved testing inferences under a general
multivariate elliptical regression model. The model is very flexible in terms
of the specification of the mean vector and the dispersion matrix, and of the
choice of the error distribution. The error terms are allowed to follow a
multivariate distribution in the class of the elliptical distributions, which
has the multivariate normal and Student-t distributions as special cases. We
obtain Skovgaard's adjusted likelihood ratio statistics and Barndorff-Nielsen's
adjusted signed likelihood ratio statistics and we conduct a simulation study.
The simulations suggest that the proposed tests display superior finite sample
behavior as compared to the standard tests. Two applications are presented in
order to illustrate the methods.
