Likelihood Methods in Statistics

-----------------------------------------------------------------------提案编号：DMS PI: Thomas A. Severini机构：西北大学项目：统计学中的似然方法摘要：本研究考虑了基于似然的统计推断中的几个问题。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的推理。本研究考虑发展对平方根似然比统计量的调整，以提高通常的正态近似的准确性，并且易于在广泛的模型中计算。这导致在一阶渐近逼近的准确性有问题的模型中改进的推理方法。该研究还研究了基于准似然函数的似然比统计的类似物。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基于预测枢轴和条件推理的一般预测方法的发展，以及预测似然方法的分析和比较，包括基于先验分布的预测密度。这项研究涉及发展准确和有用的方法，以便根据观测数据得出结论和作出预测。许多统计方法都是基于近似值；在许多情况下，这些近似的准确性是值得怀疑的。这项研究的一个方面是开发这种类型的更准确和可靠的近似。统计预测分析关注的是基于当前可用数据预测未来事件的问题。预测方法在医疗诊断、环境和全球变化、制造业和经济预测等领域有着广泛的应用。本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.