Applications and Extensions of Likelihood Methods

本文研究了基于似然推理的高阶渐近理论中的几个问题。许多高阶近似只适用于底层数据具有连续分布的情况。提出的研究考虑将这些结果扩展到底层数据具有点阵分布的情况。研究的第二个方面是开发具有层次结构的模型的方法。似然方法一般是在正确指定似然函数的假设下推导出来的。当然，在实践中，所使用的概率模型通常只是真实但未知模型的近似值。因此，提出的研究考虑了基于更有限的假设（如力矩条件）的方法的发展。基于似然函数的统计方法在统计理论和方法中起着核心作用。这些方法中的许多都是基于近似值，在某些情况下可能有可疑的准确性。本研究发展了精度普遍较高的近似方法。其结果是统计方法比目前可用的方法有了改进。

The proposed research considers several problems in the higher-order asymptotic theory of likelihood-based inference. Many higher-order approximations apply only to the case in which the underlying data have a continuous distribution. The proposed research considers the extension of these results to the case in which the underlying data have a lattice distribution. A second aspect of the research is the development of methods for models with a hierarchical structure. Likelihood methods are generally derived under the assumption that the likelihood function is correctly specified. Of course, in practice, the probability models used are often only an approximation to the true, but unknown, models. Hence, the proposed research considers the development of methods that are based on more limited assumptions, such as moment conditions. Statistical methods based on the likelihood function play a central role in statistical theory and methodology. Many of these methods are based on approximations which may have questionable accuracy in certain cases. The proposed research develops methods of approximation with generally higher accuracy. The result is statistical methods that offer an improvement over those currently available.