| Co-Investigator(Kenkyū-buntansha) |
AKAHIRA M. University of Tsukuba, 数学系, 教授 (70017424)
TAKAHASHI Y. The University of Tokyo, 教養学部, 助教授 (20033889)
KAMAE T. Osaka City University, 理学部, 教授 (80047258)
KONISHI S. The Institute of Statistical Mathematics, 統計基礎研究系, 助教授 (40090550)
HENNA J. University of the Ryukyus, 短期大学部, 助教授 (80045195)
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| Research Abstract |
The project is composed of 10 themes. We had 10 research groups for studying these themes. Members of each group are formed of resrarchers in Probability theory, Mathematical Statistics, other fields in Mathematics, Physics, Engineering, Economics and so on. Each group had symposiums. There, many new results were presented, we discussed them and researchers in different fields exchanged their opinions from different points of view. And these discussions contributed the development of reseaechs very much. The themes are as follows. 1. Application of non-standard analysis (Organizer: T.Kamae), 2. Central limit theorem (S. Ito and Y.Takahashi), 3. Information theory and related topics (S. Ihara), 4. Diophantine approximation and geodesic flow (S.Ito and Y.Takahashi), 5. Stochastic problems in Mathematical Physics (T.Shiga), 6. Methods of estimation in engineering fields (K,Iwase and S.Mase), 7. Estimation and testing statistical hypotheses in parametric models (M.Akahira and N.Inagaki), 8. Properties of estimators and related statistics (J.Henna), 9. Model analysis of data having correlation structure (S.Konishi), 10. Mathematical analysis of dynamic system and applications (S.Iwamoto)
We published the proceedings. Some of our results are: application to Fourier analysis (in Theme 1), some results on central limit theorem of mixed type (in 2), some results on entropy, large deviation and information of time series (in 3), some results on Diophantine approximation viewed form Ergodic theory (in 4), some results on percolation models and Ising models (in 5), new problems in estimation in engineering fields (in 6), higher order asymptotic efficiency of certain test statistics (in 7), distribution of coefficient of variation for non-normal populations (in 8), Baysian spproach in factor analysis (in 9), some results in Markov decision problems (in 10).
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