Bartlett-type adjustments for hypothesis testing in linear models with general error covariance matrices

Consider the problem of testing a linear hypothesis of regression coefficients in a general linear regression model with a covariance matrix involving several nuisance parameters. Then, the Bartlett-type adjustments of the Wald, Score, and modified Likelihood Ratio tests are derived for general consistent estimators of the unknown nuisance parameters. The adjusted test statistics have second-order corrections in type I errors. Simple parametric bootstrap methods are also suggested for estimating the Bartlett-type adjustments and it is shown that they have the second order accuracy.