  This paper provides general expression for Bartlett and Bartlett-type
correction factors for the likelihood ratio and gradient statistics to test the
dispersion parameter in heteroscedastic symmetric nonlinear models. This class
of regression models is potentially useful for modeling data containing
outlying observations. We consider a partition on the dispersion parameter
vector in order to test the parameters of interest. Furthermore, we develop
Monte Carlo simulations to compare the finite sample performances of the
corrected tests proposed with the usual and modified score tests, likelihood
and gradient tests, the Bartlett-type corrected score test and bootstrap
corrected tests. Our simulation results favor the score and gradient corrected
tests as well as the bootstrap tests. An empirical application is presented for
illustrative purposes.
