Likelihood Methods in Statistics

-----------------------------------------------------------------------提案编号：DMS Pi：Thomas A.Severini研究所：西北大学项目：统计学中的似然方法摘要：本研究考虑了有关基于似然的统计推断的几个问题。这些问题自然分为两个方面。第一个领域是基于似然比统计量的推理。这项研究考虑了对平方根似然比统计量的调整，以提高通常正态近似的精度，并在广泛的模型中易于计算。这导致改进了模型中的推理方法，在这些模型中，一阶渐近近似的准确性是值得怀疑的。该研究还研究了基于准似然函数的似然比统计量的类似物。第二个研究领域是统计预测分析。正在考虑的具体问题包括开发基于预测轴心和条件推理的一般预测方法，以及分析和比较预测似然方法，包括基于先验分布的预测密度。这项研究致力于发展准确和有用的方法，根据观测数据得出结论和做出预测。许多统计方法都是基于近似值的；在许多情况下，这些近似值的准确性是值得怀疑的。这项研究的一个方面是开发更准确和可靠的这种类型的近似。统计预测分析涉及基于当前可用数据预测未来事件的问题。预测方法在许多领域都有应用，包括医疗诊断、环境和全球变化、制造业和经济预测。这项研究发展了构建预测的一般方法，并研究了各种预测方法之间的关系。

----------------------------------------------------------------------- Proposal Number: DMS PI: Thomas A. Severini Institution: Northwestern University Project: Likelihood Methods in Statistics Abstract: This research considers several problems regarding likelihood-based statistical inference. These problems naturally fall into two areas. The first area is inference based on the likelihood ratio statistic. The research considers the development of an adjustment to the square-root likelihood ratio statistic that improves the accuracy of the usual normal approximation and is easily calculated in a wide range of models. This leads to improved methods of inference in models where the accuracy of first-order asymptotic approximations is questionable. The research also studies analogues of the likelihood ratio statistic that are based on a quasi-likelihood function. The second area of research is statistical prediction analysis. The specific problems being considered include the development of general methods of prediction based on predictive pivots and conditional inference, and the analysis and comparison of predictive likelihood methods, including the predictive density based on a prior distribution. This research is concerned with the development of accurate and useful methods for drawing conclusions and making predictions based on observational data. Many statistical methods are based on approximations; in many cases, the accuracy of these approximations is questionable. One aspect of this research is the development of more accurate and reliable approximations of this type. Statistical prediction analysis is concerned with the problem of predicting future events based on currently available data. Predictive methods have applications in a wide array of fields, including medical diagnosis, environment and global change, manufacturing, and economic forecasting. This research develops general methods of constructing pre dictions and studies the relationships among the various methods of prediction.