Mathematical Sciences: Semi-Parmetric Regression with Counting Data

本研究旨在建立分布特性 半参数回归中的估计和关键量 使用计数数据的模型，侧重于泊松和二项式数据 在广义线性模型的基础上。 估计数将 在具有参数化的意义上被认为是半参数的 一个组件和一个组件，这是受到一些“平滑” 约束，通常在广义样条曲线的设置中。 必须为这项研究开发必要的工具， 将本研究的结果传递给应用型医学家 是光滑一般线性方程组的有效计算方法 模型问题，其中设计点落在一个规则， 多维网格 统计分布理论的研究将 提供有用的分析工具，直接转化为 选择概率模型的图解程序， 诊断程序，以评估其充分性。 这 研究的方向是简单的参数 计数数据的模型是没有保证的。

This research is to establish the distributional properties of estimates and pivotal quantities in semi-parametric regression models with counting data, focusing on Poisson and binomial data in the setting of the generalized linear model. Estimates will be considered semi-parametric in the sense of having a parametric component and a component which is subject to some "smoothing" constraint, usually in the setting of generalized splines. Necessary tools that must be developed for this research and for transfering results from this research to the applied statisician are efficient computational methods for smooth general linear model problems in which the design points fall on a regular, multidimensional grid. This research in statistical distribution theory will provide useful analytical tools which translate directly into graphical procedures for selecting probability models and diagnostic procedures for assessing their adequacy. This research is directed toward situations where simple parametric models of counting data are not warranted.