Application of elementary differential geometry to influence analysis (Q2919633)

The first part of this textbook with the title ``Geometry'' presents an introduction to the geometry of graphs, including the concepts of normal curvature, sectional curvature, Ricci curvature and Gaussian curvature. The second part, ``Statistics'', provides a background of statistical concepts and basic models that form the fundamental knowledge necessary for a better comprehension of the concept of ``local influence'', namely ``bivariate and multivariate distribution'' and ``linear regression analysis''. The aim of the book is to apply the geometry of graphs to analyze functions arising from concrete problems, such as through statistics. Many statistical analyses involve a hypothesized model. But the statistical inference is affected by the hypothesized model and the data collected. Therefore, it is important to study the perturbation of various aspects of the model, which can be represented by a set of perturbation parameters and therefore it is necessary to apply geometric concepts to study this function. In the last part ``Local influence analysis'', one can find measures for the influence of individual perturbation parameters. Various measures generated by a local perturbation to assess the influence of the perturbation of model inputs are developed.NEWLINENEWLINE This textbook is intended for the use of senior undergraduate and graduate students in mathematics or in statistics. It has an inter-disciplinary character and facilitate interaction, collaboration and innovative research activities among mathematical scientists.