Mathematical Sciences: Dual Geometries and Their Applicationto Generalized Linear Models

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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.