Mathematical Sciences: Dual Geometries and Their Applicationto Generalized Linear Models

这项研究将通过扩展用于研究正规线性模型的欧几里德几何来开发广义线性模型的几何结构。这种几何方法将被用来研究广义线性模型的估计算法、影响和局部性质。将寻求一种替代字符串的几何方法。这项研究使用几何来研究线性模型的统计量，其中常见的正态假设已被推广。几何技术有望有助于综合这些广义假设下估计的性质和行为。

This research will develop a geometric structure for generalized linear models by extending the Euclidean geometry used to study the normal linear model. This geometric approach will be used to study estimation algorithms, influence, and the local properties of generalized linear models. A geometric alternative to strings will be sought. This research uses geometry to study the statistics of linear models in which the common assumption of normality has been generalized. Geometric techniques promise to be helpful in synthesizing the properties and behavior of estimates under these generalized assumptions.