Bartlett corrections and bias correction for two heteroscedastic regression models

Abstract

We present, in matrix notation, general Bartlett correction formulae for several hypotheses in the multiplicative and dependent variable heteroscedastic regression models. The formulae are simple enough to be used analytically to obtain several closed-form expressions in special cases. They have also advantages for numerical purposes. Improved likelihood ratio tests are discussed for several test problems in these models. By simulation, the performance of the Bartlett corrections is illustrated. We derive general formulae for the n⁻¹ bias of the maximum likelihood estimates in these models, where n is the sample size.