Mathematical Sciences: Semiparametric Models & Estimation of Survival Functions

本研究的两个方面分别是半参数回归模型和估计量的性质以及不同方法的比较优劣。在生存函数分析的背景下，估计问题集中在截尾分布和/或观测截尾时间中的信息。在工业环境中，问题集中在描述Bootstrap方法在平滑和确定在什么情况下这是更好的方法中使用的行为上。根据已确定的因素或属性只能部分描述统计模型或功能的情况普遍存在。这个项目考虑了医学试验数据的应用，以及工业实验数据的应用。当已知特征仅指定模型的一部分时，可以用多种不同的方式来描述未解释的部分。这项建议旨在确定哪些条件使每一种特定的方法选择都足够优越，从而使其使用变得重要。

The two aspects of this research focus on semiparametric regression modeling and the properties of estimators and the comparative merits of different approaches. In the context of survival function analysis, the estimation problem focuses on the information in the censoring distribution and/or the observed censoring times. In the industrial context, the problem focuses on describing the behavior of the bootstrap methodology as used in smoothing and in determining conditions under which this is the superior methodology. Situations in which statistical models or functions can be described only partially in terms of identified factors or attributes occur widely. This project considers applications to data from medical trials and, separately, from industrial experimentation. When known features only specify part of the model, the unexplained part can be described in a number of different ways. This proposal seeks to identify the conditions which make each particular choice of methodology are sufficiently superior to make its use important.