Application of elementary differential geometry to influence analysis
type: Item
instance of: scholarly article
zbMATH Open document ID: 1266.53002
author: Yat-Sun Poon
author: Wai-Yin Poon
publication date: 2012-10-05T00:00:00Z
Mathematics Subject Classification ID: 53-02
Mathematics Subject Classification ID: 53A07
Mathematics Subject Classification ID: 53A30
Mathematics Subject Classification ID: 53A45
Mathematics Subject Classification ID: 53B20
Mathematics Subject Classification ID: 60E05
Mathematics Subject Classification ID: 62E99
Mathematics Subject Classification ID: 62J05
zbMATH DE Number: 6090388
zbMATH Keywords: Euclidean geometry
zbMATH Keywords: random variables
zbMATH Keywords: bivariate and multivariate distribution
zbMATH Keywords: linear regression analysis
zbMATH Keywords: local influence analysis
MaRDI profile type: Publication
title: Application of elementary differential geometry to influence analysis
published in: Surveys of Modern Mathematics
review text: 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.
reviewed by: T. Postelnicu
description: scientific article; zbMATH DE number 6090388