The Encompassing Principle and Hypothesis Testing
利用指数倾斜密度族，探讨涵盖原理与M检验或条件矩检验原理的关系，证明两者可产生相同检验统计量，但动机和侧重点不同，对计量经济建模重要。
The exponentially tilted family of densities is used to discuss the relationship between the encompassing principle and the M -test or conditional moment testing principle. It is shown that the two principles are capable of generating the same test statistics and in this sense equivalent. However, there are differences in motivation and emphasis underlying the principles that are important in econometric modeling. In addition, parsimonious encompassing interpretations for test statistics, including those of Cox (1961, in Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability I , pp. 105-123; 1962, Journal of the Royal Statistical Society, Series B 24, 406-424) and Atkinson (1970, Journal of the Royal Statistical Society, Series B 32, 323-344) are provided.