Abstract
In this note we consider the distributions of the Wald, likelihood ratio and Lagrange multiplier statistics in the classical linear regression model. It is shown that the finite sample distribution of each test statistic can be written as a member of the generalized beta model introduced by McDonald and Xu (1995b). This facilitates exact inference and is useful in understanding how the distribution of each statistic changes with different parameter values. For example, this characterization makes it clear that Wald tests may severely overreject the null hypothesis in some cases and reveals the fact that the Lagrange multiplier statistic has a distribution with bounded support.
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