| Project/Area Number |
14540124
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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 Kochi University, Faculty of Science, Professor, 理学部, 教授 (60124806)
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| Co-Investigator(Kenkyū-buntansha) |
KIKUCHI Yasuki Nagasaki University, School of Health Science, Associate Professor, 医学部, 助教授 (10124140)
OHTSUBO Yoshio Kochi University, Faculty of Science, Professor, 理学部, 教授 (20136360)
NIIZEKI Shozo Kochi University, Faculty of Science, Professor, 理学部, 教授 (60036572)
ANRAKU Kazuo Seinan Gakuin University, Division of Childfood Education, Professor, 文学部, 教授 (90184332)
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| Project Period (FY) |
2002 – 2003
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| Project Status |
Completed (Fiscal Year 2003)
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| Budget Amount *help |
¥3,600,000 (Direct Cost: ¥3,600,000)
Fiscal Year 2003: ¥1,500,000 (Direct Cost: ¥1,500,000)
Fiscal Year 2002: ¥2,100,000 (Direct Cost: ¥2,100,000)
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| Keywords | incomplete data / Weibull distribution / EM algorithm / generalized EM algorithm / MLE / order restriction / simple order / PAVA / 最尤推定量 / 統計的順序制約問題 / 情報量基準 / Weibull分布 / 生存関数 / スターリングの公式 / 位相空間 / 離散時間確率過程 / 潜在マルコフモデル / ポアソン混合型分布 / 双対問題 / ガウス積分 / 各点収束 |
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| Research Abstract |
The summary of research results is as follows.
1.In survival time analysis, we usually suppose Weibull distribution, which is a generalization of exponential distribution. We think that Weibullization of gamma distribution would be effective. Survival time data have censored one, and those are incomplete data. Since it is natural to apply EM-approach, we propose such a procedure.
2.We consider the convergence conditions for Generalized Expectation-Maximization(GEM) algorithm. Wu(1983, A.S.) gave conditions for EM to converge to MLE. But, we have already given a counter example which does not converge to the MLE, but satisfies Wu's conditions. We give moreover the correction of his proof for the convergence of EM.
3.In the simple order restricted statistical inference problem, PAVA algorithm is famous for its simplicity. But, this problem is also famous for the difficulty without simple order restriction or independency of the components. Dykstra(A.S.) proposes an iterative procedure by repeating PAVA algorithm. In our study, considering the dual of his procedure, we show that the proof of the convergence is easily given and the amount of calculation is drastically reduced.
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