Admissibility of the Likelihood Ratio Test when the Parameter Space is Restricted under the Alternative
证明当备择假设下参数空间受限时，似然比检验是可容许的，且对远离原假设的备择假设具有最大功效，适用于高斯线性回归和动态非线性模型。
This paper considers hypothesis tests when the parameter space is restricted under the alternative hypothesis. Multivariate one-sided tests are a leading example. The likelihood ratio (LR) test is shown to be admissible and to maximize power against alternatives that are arbitrarily distant from the null hypothesis. Exact results are established first for Gaussian linear regression models with known variance. Asymptotic analogues are then established for dynamic nonlinear models.