2001 Fiscal Year Final Research Report Summary
Statistical inference based on incomplete data
| Project/Area Number |
11640127
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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 | Kochi University |
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Principal Investigator |
NOMAKUCHI Kentaro Faculty of Science, Kochi University, Professor, 理学部, 教授 (60124806)
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| Co-Investigator(Kenkyū-buntansha) |
SAKATA Toshio Department of Industrial Design, Kyushu Institute of Design, Professor, 芸術工学部, 教授 (20117352)
OHTSUBO Yoshio Faculty of Science, Kochi University, Professor, 理学部, 教授 (20136360)
NIIZEKI Shozo Faculty of Science, Kochi University, Professor, 理学部, 教授 (60036572)
ANRAKU Kazuo Division of Childhood Education. Seinan Gakuin University, Professor, 文学部, 教授 (90184332)
KIKUCHI Yasuki School of Health Science, Nagasaki University, Associate Professor, 医学部, 助教授 (10124140)
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| Project Period (FY) |
1999 – 2001
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| Keywords | hidden Markov model / Markov chain / EM algorithm / generalized EM algorithm / MLE / order restriction / stochastically larger / Gibbs sampling |
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| Research Abstract |
The summary of reserch results is as follows.
1. We give two modifications of a hidden Markov (HM) model. One modification is obtained by combining an HM model with an autoregressive process in the data generation part. The other modification is obtained by assuming a second-order Markov chain in the system state process. We examine the identifiability of the three models, which means that each model has data to be better fitting than the others. And we conclude that the first modification has a good performance.
2. We consider the convergence conditions for Generalized Expectation-Maximization (GEM) algorithm, which is used to calculate Maximum Likelihood Estimate (MLE). The EM-algorithm users believe that Wu(1983, A.S.) gives fundamental conditions for the convergence of GEM. We, however, give a counter example which does not converge to the MLE, but satisfies Wu's conditions.
3. In the order restricted statistical inference problem, we prove that moments of the distance between a true parameter and the least square estimate are non-decreasing when the true parameter moves along a half line from an initial point in the null space. This follows from "stochastically larger" property of the distance.
4. We consider the maximum likelihood estimation (MLE) of correlation matrix under order restrictions among correlations. We can reach the MLE by repeating alternately the two maximization process : (A) maximization with respect to correlation matrix and (B) maximization with respect to variance. In the maximization process (A), we use Gibbs sampling to generate uniformly distributed random correlation matrices on the hypothesis space.
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