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Abstract:
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Directional testing of vector parameters, based on higher order approximations of likelihood theory, can ensure extremely accurate inference, even in high-dimensional settings where standard first order likelihood results can perform poorly. Here we explore examples of directional inference where the calculations can be simplified, and prove that in several classical situations the directional test reproduces exact results based on $F$-tests. These findings give a new interpretation of some classical results and support the use of directional testing in general models, where exact solutions are typically not available.
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