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Study of the theory of statistical multivariate analysis and its application to economic analysis

统计多元分析理论及其在经济分析中的应用研究

基本信息

批准号：
02630011
负责人：
TAKEMURA Akimichi
金额：
$ 1.34万
依托单位：
University of Tokyo
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1990
资助国家：
日本
起止时间：
1990 至 1992
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-02630011/
关键词：
MULTIVARIATE ANALYSIS LIKELIHOOD RATIO TEST ADMISSIBILITY 分散行列の推定非許容性 Zonal多項式

项目摘要

This project focused on theoretical study of multivariate analysis in the framework of multivariate normal distribution and the investigation of the assumption of multivariate normality. During the period of this study this author published two textbooks, "Introduction to Multivariate Statistical Inference" (Kyoritsu shuppan) and "Modern Mathematical Statistics" (Soubunsha). The former presents this authors's view of the theoretical framework and the recent important developments of multivariate analysis in a concise and self-contained manner. The latter is a readable textbook on the theory of mathematical statistics including graduate level materials. Concerning the theoretical study of multivariate analysis this author published a survey paper on zonal polynomials continuing his study on the subject. In a joint paper with Yo Sheena this author published a paper concerning the admissibility of orthogonally invariant estimator in the estimation of covariance matrix of a multivariate normal population. On the test of equality of covariance matrices this author gave a detailed decomposition of the likelihood ratio test (to appear). For the investigation of the multivariate normality this author discussed joint higher order moments in the framework of orthogonal invariance and derived the maximal invariants. Based on the invariant third order moments this author proposed a test of multivariate normality (to appear). Thus useful results on multivariate analysis have been obtained in this project. On the other hand concrete results on multivariate time series models and its application to economic analysis have not yet been obtained as planned in this project.

本项目主要研究多元正态分布框架下的多元分析理论和多元正态假设的研究。在本研究期间，作者出版了两本教科书，《多元统计推断导论》（共立书）和《现代数理统计》（总论社）。前者提出了作者的观点的理论框架和最近的重要发展多元分析在一个简洁和自足的方式。后者是一本关于数理统计理论的可读教科书，包括研究生水平的材料。关于多元分析的理论研究，作者发表了一篇关于带状多项式的综述论文，继续他在这方面的研究。在与Yo Sheena的联合论文中，作者发表了一篇关于多元正态总体协方差矩阵估计中正交不变估计的可接受性的论文。关于协方差矩阵的相等性检验，作者给出了似然比检验的详细分解。为了研究多元正态性，本文在正交不变性的框架下讨论了联合高阶矩，导出了最大不变量。基于不变三阶矩，提出了一种多元正态性检验方法。因此，本项目在多元分析方面取得了有益的结果。另一方面，本项目尚未按计划取得关于多元时间序列模型及其在经济分析中的应用的具体成果。