| Project/Area Number |
08680327
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Statistical science
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| Research Institution | University of Tokyo |
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Principal Investigator |
TAKEMURA Akimichi University of Tokyo, Faculty of Economics, Professor, 大学院・経済学研究科, 教授 (10171670)
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| Co-Investigator(Kenkyū-buntansha) |
KUBOKAWA Tatsuya University of Tokyo, Faculty of Economics, Assoclate Professor, 大学院・経済学研究科, 助教授 (20195499)
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| Project Period (FY) |
1996 – 1997
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| Project Status |
Completed (Fiscal Year 1997)
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| Budget Amount *help |
¥2,400,000 (Direct Cost: ¥2,400,000)
Fiscal Year 1997: ¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 1996: ¥1,100,000 (Direct Cost: ¥1,100,000)
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| Keywords | Asymptotic expansion / shrinkage / Likelihood Ratio / MANOVA / Bartlett correction / Heteroscedasticity / Shrinkage estimator |
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| Research Abstract |
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.
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