Applications and Extensions of Likelihood Methods

似然法的应用和扩展

• 批准号: 0102274
• 负责人: Thomas Severini
• 金额: $ 8.39万
• 依托单位: Northwestern University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-08-15 至 2005-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0102274&HistoricalAwards=false
• 关键词: Applications; Extensions; Likelihood; Methods

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.

所提出的研究考虑了基于似然推理的高阶渐近理论中的几个问题。许多高阶近似仅适用于基础数据具有连续分布的情况。拟议的研究考虑将这些结果扩展到基础数据具有格子分布的情况。研究的第二个方面是开发具有层次结构的模型方法。似然方法通常是在正确指定似然函数的假设下导出的。当然，在实践中，所使用的概率模型通常只是真实但未知的模型的近似。因此，拟议的研究考虑开发基于更有限的假设（例如矩条件）的方法。 基于似然函数的统计方法在统计理论和方法中发挥着核心作用。许多这些方法都是基于近似值，在某些情况下其准确性可能存在问题。所提出的研究开发了精度普遍更高的近似方法。 其结果是统计方法比目前可用的方法有所改进。