Aplicações da geometria riemanniana em estatística matemática

• Autor(a) principal: Barrêto, Felipe Fernando ângelo
• Data de Publicação: 2013
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações da UFPB
• Texto Completo: https://repositorio.ufpb.br/jspui/handle/tede/7422
• topic: Medida de Influência; Variedade de Perturbação; Tensor métrico; Curvatura; Modelo paramétrico; Conexão afim; Infuence Measure; Perturbation manifold; Metric tensor; Curvature; Parametric model; Affine connection; CIENCIAS EXATAS E DA TERRA::MATEMATICA

Cook's local infuence approach based on normal curvature is an important diagnostic tool for assessing local infuence of minor perturbations to a statistical model. However, no rigorous approach has been developed to address two fundamental issues: the selection of an appropriate perturbation and the development of infuence measures for objective functions at a point with a nonzero rst derivative. The aim of this paper is to develop a diferential-geometrical framework of a perturbation model (called the perturbation manifold) and utilize associated metric tensor and ane curvatures to resolve these issues. We will show that the metric tensor of the perturbation manifold provides important information about selecting an appropriate perturbation of a model.