Global and Partial Non-Nested Hypotheses and Asymptotic Local Power
通过概率密度函数的“接近度”度量，将假设分为嵌套、全局非嵌套和部分非嵌套三类，并证明仅在部分非嵌套情形下可定义局部备择假设，进而推导出Cox检验统计量在局部备择假设下的渐近正态分布。
This paper addresses two related issues in the literature of non-nested hypotheses testing. Firstly, by means of a measure of “closeness” of probability density functions, it shows how any two hypotheses can be placed into the nested and the non-nested categories with the latter category being subdivided further into “globally” and “partially” non-nested hypotheses. Secondly, by emphasizing the distinction between a “local null” and a “local alternative,” the paper shows that only in the case of partially non-nested hypotheses is it possible to specify local alternatives. In this case the paper derives the asymptotic distribution of the Cox test statistic under local alternatives and shows that it is distributed as a normal variate with a mean which is directly related to the measure of “closeness” of the alternative to the null hypothesis.