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. The Canadian Journal of Statistics 47: 619–627; 2019 © 2019 Statistical Society of Canada

中文翻译：

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定向考察F检验

矢量参数的定向测试基于似然理论的高阶近似，即使在标准一阶似然结果表现不佳的高维环境中，也可以确保极其精确的推断。在这里，我们探索了可以简化计算的方向推断示例，并证明了在几种经典情况下，方向测试可以基于F检验重现精确的结果。这些发现为一些经典结果提供了新的解释，并支持在一般模型中使用定向测试，而通常无法获得精确的解决方案。《加拿大统计杂志》 47：619–627；2019©2019加拿大统计学会