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

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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.