1998 Fiscal Year Final Research Report Summary
Research of Information-geometric Properties in Statistical Estimation Theory
| Project/Area Number |
09640264
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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 |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Osaka University |
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Principal Investigator |
INAGAKI Nobuo OSAKA UNIV., GRAD.SCH.OF ENG.SCI., PROFESSOR, 大学院・基礎工学研究科, 教授 (10000184)
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| Co-Investigator(Kenkyū-buntansha) |
KUMAGAI Etsuo OSAKA UNIVERSITY,GRAD.SCH.OF ENG.SCI., ASSIST.PROF., 大学院・基礎工学研究科, 助手 (20273617)
AKI Shigeo OSAKA UNIVERSITY,GRAD.SCH.OF ENG.SCI., ASS.PROFESSOR, 大学院・基礎工学研究科, 助教授 (90132696)
TANIGUCHI Masanobu OSAKA UNIVERSITY,GRAD.SCH.OF ENG.SCI., ASS.PROF., 大学院・基礎工学研究科, 助教授 (00116625)
ISOGAI Takafumi OSAKA UNIVERSITY,GRAD.SCH.OF ENG.SCI., ASS.FROF., 大学院・基礎工学研究科, 助教授 (00109860)
SHIRAHATA Shingo OSAKA UNIVERSITY,GRAD.SCH.OF ENG.SCI., PROFESSOR, 大学院・基礎工学研究科, 教授 (10037294)
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| Project Period (FY) |
1997 – 1998
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| Keywords | Maximum likelihood estimator / Fisher Information / Information loss / Statistical curvature / Circular Mechanism of likelihood / Information geometry / Multidimensional sphere model / Generalized linear regression model |
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| Research Abstract |
We studied information-geometric properties in the statistical estimation theory under the following three themes
(1) The information loss of the maximum likelihood estimator and its information-geometric aspects (by N.INAGAKI and E.KUMAGAI) The asymptotic representaion of the information loss of the maximum likelihood estimator is shown by B.Efron and S.Amari due to the statistical curvature and Fisher information. We obtained an algorism to calculate the center and radius with the statistical curvature which we call the circular mechanism of the likelihood function. We discussed the multidimensional sphere model as the extensions of Fisher' s circle and sphere models for 2 and 3 dimen sions, respectively. We obtained the exact infromation loss of the maximum likelihood estimator of the angle parameter in the k-dimensional sphere model and showed its asymptotic behavior which converges to the Efron-Amari' s asymptotic re-presentation. We studied the duality of parameter and observation in the exponential type of distributions by the Legendre convex duality of the cumulant generating function, which leads to the asymptotic properties of maximum likelihood estimator.
(2) Estimation problems in spacial data and time series analysis (T.ISOGAI and M.TANIGUCHI) : The regression problems of spacial data were studied due to parametric and empirical variograms. We had many results for time series analysis, prediction theory and their applications.
(3) Estimation problems in generalized linear models (S.SHIRAHATA and S.AKI) Topics of dose response analysis, life time analysis, and so on, and applications of gene-ralized linear models were studied.
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Research Products
(18 results)
