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This paper provides general expression for Bartlett and Bartlett-typecorrection factors for the likelihood ratio and gradient statistics to test thedispersion parameter in heteroscedastic symmetric nonlinear models. This classof regression models is potentially useful for modeling data containingoutlying observations. We consider a partition on the dispersion parametervector in order to test the parameters of interest. Furthermore, we developMonte Carlo simulations to compare the finite sample performances of thecorrected tests proposed with the usual and modified score tests, likelihoodand gradient tests, the Bartlett-type corrected score test and bootstrapcorrected tests. Our simulation results favor the score and gradient correctedtests as well as the bootstrap tests. An empirical application is presented forillustrative purposes.

Bartlett and Bartlett-type corrections in heteroscedastic symmetric nonlinear regression models