Introduction

The linear regression model with a nonscalar error covariance matrix is usually estimated by Generalized Least Squares (GLS). Conventional F and t-testing procedures of any linear hypotheses on the parameters for this model is justified under the implicit assumption that the sample size is large enough to permit inference on the parameters estimates based on the chi-square or normal distributions. However, the possibility of erroneous inferences in finite samples is always present, and it can be attributed to the existence of considerable discrepancy between the actual and the nominal size of the asymptotic chi-square or normal tests. Since the differences between the actual and nominal size tend to be large in finite samples, compared with the differences in power (see Rothenberg, 1982), size corrections are suggested to eliminate most of the probability of conflict among the alternative testing procedures (see Rothenberg, 1984b, 1988, and Magdalinos and Symeonides, 1995). In particular, Rothenberg (1984b, 1988) derived general formulae giving the Edgeworth-corrected critical values for the Wald and t-test statistics based on Edgeworth expansions of their corresponding asymptotic, chi-square and normal distributions, respectively. This is done for a wide class of regression models used in practice. Instead of using the asymptotic form of the tests, Magdalinos and Symeonides (1995, 1996) recommended to use the degrees of freedom adjusted forms of the above statistics and derived expansions in terms of the F and t distributions, respectively.