The Encompassing Principle and its Application to Testing Non-Nested Hypotheses
提出涵盖原则，统一了非嵌套检验的文献，能轻松建立检验间的等价关系，并引入隐含原假设概念，揭示某些检验的有效接受区域超出名义原假设，导致对固定备择假设不一致。以两个非嵌套线性回归模型为例，说明F检验和所有单自由度非嵌套检验都有涵盖解释。
The encompassing principle is used to develop a testing framework which unifies the literature on non-nested testing, allowing analysis of the relationship between alternative tests and in particular enabling asymptotic and finite sample equivalences and identities to be established easily when they exist, as well as embracing nested hypothesis testing. The concept of the implicit null hypothesis of a test is introduced to show that the effective acceptance region for some tests extends beyond the acceptance region corresponding to the null of interest, and so such tests can be inconsistent against fixed alternatives closely related to the nominal null and alternative. The analysis is illustrated by an application to two non-nested linear regression models, and it is shown that the conventional F test, as well as all the one degree of freedom non-nested tests, has an encompassing interpretation, and that the F test is a complete parametric encompassing test.