The Asymptotic Local Structure of the Cox Modified Likelihood-Ratio Statistic for Testing Non-Nested Hypotheses
证明了Cox修正似然比统计量在数据生成过程收敛到两个假设交集时，渐近等价于非退化渐近正态随机向量的双线性形式，并纠正了文献中关于其渐近局部正态性的错误假设。
It is shown that the Cox modified likelihood-ratio statistic for testing partially non-nested hypotheses H 0 and H 1 is asymptotically equivalent to a bilinear form in nondegenerate asymptotically normal random vectors for sequences of data-generating processes converging to the intersection of H 0 and H 1 but not necessarily belonging to either H 0 or H 1 . One of the asymptotically normal vectors is the complete parametric encompassing vector of Mizon and Richard, while the other is a close relative. The results are valid regardless of whether or not the data-generating process is exponential and imply that the Cox statistic is not generally asymptotically locally normal. This corrects an assumption made in recent literature.