1996 Fiscal Year Final Research Report Summary
Evaluation of Predictive Distributions based on Information and Entropy
| Project/Area Number |
08454043
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | KYUSYU UNIVERSITY |
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Principal Investigator |
KONISHI Sadanori Kyushu Univ.Graduate School of Math.Professor, 大学院・数理学研究科, 教授 (40090550)
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| Co-Investigator(Kenkyū-buntansha) |
FUEDA Kaoru Kyushu Univ.Graduate School of Math.Kyushu University Research Associate, 大学院・数理学研究科, 助手 (50253399)
NAKAO Mituhiro Kyushu Univ.Graduate School of Math.Kyushu University Professor, 大学院・数理学研究科, 教授 (10136418)
TANAKA Shun-ichi Kyushu Univ.Graduate School of Math.Kyushu University Professor, 大学院・数理学研究科, 教授 (00028127)
YANAGAWA Takashi Kyushu Univ.Graduate School of Math.Kyushu University Professor, 大学院・数理学研究科, 教授 (80029488)
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| Project Period (FY) |
1996
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| Keywords | Information Criteria / Bootstrap Methods / Nonlinear Models / Equivalence tests / Elliptic Boundary Value Problems / Numerical Solution with Guaranteed Error Bounds / Object-Intensive Language / Nonparametric Tests |
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| Research Abstract |
The purpose of the research is to investigate the problem of evaluating the goodness of statistical models from an information-theoretic point of view. The following are the main results obtained through this research project extending over 1996.
1. Information criteria were proposed for evaluating statistical models constructed by various estimation procedures when the specified family of probability distributions does not contain the distribution generating the data. The proposed criteria are applied to the evaluation of models estimated by maximum likelihood, robust, penalized likelihood, Bays procedures, etc. In regard to computer-intensive methods the theoretical and practical aspects of the use of the bootstrap were investigated in model evaluation problems. 2. Equivalence tests for binary data with pair-matched design in clinical trials were explored. Eight tests were investigated altogether including those tests constructed by the GSK method, the tests which use estimated null variances among others. 3. A numerical enclosure method with guaranteed L^* error bounds for the solution of nonlinear elliptic problems of second order were investigated. Using an a posteriori error estimates for the approximate solution of the problem with higher order C^0-finite element, it was shown that we can obtain the guaranteed L^* error boundswith high accuracy. 4. The verification procedure were extended to nondifferentiable nonlinear elliptic problem related to MHD equilibra, and a computing algorithm which automatically encloses the solution with guaranteed error bounds was constructed. 5. Unified construction procedure of class of rank tests were investigated and the asymptotic normality was proved for test statistics for the two-sample problem derived by the convex sum distance.
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