  The problem of reducing the bias of maximum likelihood estimator in a general
multivariate elliptical regression model is considered. The model is very
flexible and allows the mean vector and the dispersion matrix to have
parameters in common. Many frequently used models are special cases of this
general formulation, namely: errors-in-variables models, nonlinear
mixed-effects models, heteroscedastic nonlinear models, among others. In any of
these models, the vector of the errors may have any multivariate elliptical
distribution. We obtain the second-order bias of the maximum likelihood
estimator, a bias-corrected estimator, and a bias-reduced estimator. Simulation
results indicate the effectiveness of the bias correction and bias reduction
schemes.
