Structures of symmetry for discrete and continuous multivariate analysis and its combination

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K05006
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Tokyo University of Science
• Principal Investigator: Tomizawa Sadao 東京理科大学, 理工学部情報科学科, 教授 (50188778)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: 分割表統計解析 / 離散多変量解析

Outline of Final Research Achievements

For discrete multivariate analysis (statistical analysis of contingency tables) and continuous multivariate analysis, we considered some models of symmetry and their decompositions, and considered the combination of structure of symmetry for both multivariate analysis.
(1)For multi-way contingency tables, we proposed the models of various symmetry. Also we proposed the measures to represent the degree of departure from model, and considered the decomposition of mesure. (2)For multivariate probability density functions, we gave the definition of density function of symmetry and point-symmetry, and gave the decomposition of its density function.

Free Research Field

数理統計学