Decision theoretic approach to computer intensive methods of multivariate analysis

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First we summarize research results by the head investigator Akimichi Takemura. He has published with the co-author Satoshi Kuriki the paper "A proof of independent Bartlett correctability of nested likelihood ratio tests" in Annals of Institute of Statistical Mathematics. This paper proves that the likelihood ratio statistics for nested hypotheses can be Bartlett-corrected independently of each other. His paper with the co-author Toshio Honda "The effect of heteroscedasticity on the actual size of Chow test" appeared in Journal of the Japan Statistical Society. In this paper he has obtained results on the actual signigicance levels of the test of structural change (Chow test), when the error terms of the regression model has heteroscedasticity. His paper with Hidehiko Kamiya titled "On rankings generated by pairwise linear discriminant analysis of m populations" appeated in the Journal of Multivariate Analysis. This paper investigates the number of rankings and properties of non-appearing rankings in detail based on the theory of hyperplane arrangements. His most recent publication "Weights of chi distribution for smooth or piecewise smooth cone alternattives. The annals of statistics" in the Annals of Statistics investigates the weights of chi-bar-squared distribution for smooth convex cone alternatives using differential geometric methods.Next we summarize research results by Tatsuya Kubokawa. His paper with M.S.Srivastava titled "Double shrinkage estimators of ratio of variances" appeared in the Proceedings of the Sixth Eugene Lukacs Symposium. This paper gives a new shrinkage estimator for the ratio of variances. Furthermore "Shrinkage estimators in a mixed MANOVA and GMANOVA model" by Y.Kubokawa, and A.K.Md.E.Saleh compares shrinkage estimators in Multivariate Analysis Variance Model and its generalizations.