| Project/Area Number |
12554002
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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 | 展開研究 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | University of Tsukuba |
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Principal Investigator |
AKIHIRA Masafumi University of Tsukuba, Institute of Mathematics, Professor, 数学系, 教授 (70017424)
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| Co-Investigator(Kenkyū-buntansha) |
SHIRAKURA Teruhiro Kobe University, Faculty of Education, Professor, 発達科学部, 教授 (30033913)
TERUI Akira University of Tsukuba, Institute of Mathematics, Research Assistant, 数学系, 助手 (80323260)
AOSHIMA Makoto University of Tsukuba, Institute of Mathematics, Associate Professor, 数学系, 助教授 (90246679)
KONNO Yoshihiko Japan Woman's University, Faculty of Science, Associate Professor, 理学部, 助教授 (00205577)
TAGURI Masaaki Chiba University, Faculty of Science, Professor, 理学部, 教授 (10009607)
高橋 邦彦 筑波大学, 数学系, 助手 (50323259)
河合 伸一 防災科学技術研究所, 先端解析技術研究部, 主任研究員
景山 三平 広島大学, 教育学部, 教授 (70033892)
庄野 宏 農水省遠洋水産研究所, 浮魚資源部, 研究員
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| Project Period (FY) |
2000 – 2003
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| Project Status |
Completed (Fiscal Year 2003)
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| Budget Amount *help |
¥13,700,000 (Direct Cost: ¥13,700,000)
Fiscal Year 2003: ¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 2002: ¥3,200,000 (Direct Cost: ¥3,200,000)
Fiscal Year 2001: ¥3,200,000 (Direct Cost: ¥3,200,000)
Fiscal Year 2000: ¥3,800,000 (Direct Cost: ¥3,800,000)
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| Keywords | Interval estimation / Testing hypothesis / Maximum likelihood estimator / Risk / Bootstrap / Bayesian method / Experimental design / Combinatorics / 実験的計画法 / 配置の理論 / 離散数学 / グラフ理論 / 符号理論 / 識別アルゴリズム / ラテン方格 / 回帰係数 / p値 / ベイズ解 / ミニマックス / 最大推定量 / 区間予測 / 枢軸法 / 完備十分統計量 / 被覆確率 / 量子ガウス状態 / 逐次標本抽出計画 / 多重比較法 / 飽和型直交配列 / 直交表 / 最適計画 / 検定 / マックスミン計画 / 量子推定 / 効率 |
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| Research Abstract |
The investigation on various themes was systematically done, in cooperation with researchers in related areas to statistical region estimation, as follows. (1) On the development of procedures, in the experimental design and its periphery, and the application, interesting results are obtained. (2) On the development of procedures on statistical region estimation and its application are closely studied. (3) The theory of computer-oriented statistical procedures and its application are examined in detail, new knowledge on the comparison of estimation procedures is obtained, and more accurate procedures are developed. (4) The resolution of the combinatorial structure of experimental design and its periphery and the application are closely studied, the procedures are developed, and practically useful procedures are investigated. In particular, in the experimental physics etc., there are many cases where a parameter is essentially assumed to be theoretically positive (or nonnegative} valued
… More
. Then there is a problem to make an interval estimation of an unknown parameter from the observation with errors. If the errors have the same magnitude as the value of the unknown parameter, then the ordinary confidence interval involves a negative part since it disregards that the parameter is positive valued, and the interval can be an empty set provided that the parameter is restricted to be positive. On the problem physicists proposed many ways to construct confidence intervals, but from the viewpoint of statistical region estimation, there are Bayesian and non-Bayesian angles. In the Bayesian case, it is enough to confine the prior distribution to the region of the existence of the parameter. In the investigation, the combined Bayesian-frequentist approach is proposed to construct the confidence interval for a restricted parameter. Comparing the method with usual pivotal and likelihood ones, it is examined to be reasonable. And a research toward the practice by the new method is also done Less
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