Project/Area Number  10304005 
Research Category 
GrantinAid for Scientific Research (A).

Section  一般 
Research Field 
General mathematics (including Probability theory/Statistical mathematics)

Research Institution  University of Tsukuba 
Principal Investigator 
AKAHIRA Masafumi University of Tsukuba, Institute of Mathematics, Professor, 数学系, 教授 (70017424)

CoInvestigator(Kenkyūbuntansha) 
谷口 正信 大阪大学, 基礎工学研究科, 助教授 (00116625)
久保川 達也 東京大学, 経済学部, 助教授 (20195499)
AOSHIMA Makoto University of Tsukuba, Institute of Mathematics, Associate Professor, 数学系, 助教授 (90246679)
FUJIKOSHI Yasunori Hiroshima University, Department of Mathematics, Professor, 理学部, 教授 (40033849)
磯貝 英一 新潟大学, 理学部, 教授 (40108014)
YOSHIDA Nakahiro University of Tokyo, Department of Mathmatical Sciences, Associate Professor, 数理科学研究科, 助教授 (90210707)
高田 佳和 熊本大学, 工学部, 教授 (70114098)
KOIKE Kenichi University of Tsukuba, Institute of Mathematics, Assistant Professor, 数学系, 講師 (90260471)
間瀬 茂 東京工業大学, 理学部, 教授 (70108190)
大和 元 鹿児島大学, 理学部, 教授 (90041227)
狩野 裕 大阪大学, 人間科学部, 助教授 (20201436)
栗木 哲 統計数理研究所, 助教授 (90195545)
SHIRAISHI Takaaki Yokohama City University, Department of Mathmatical Sciences, Professor, 理学部, 教授 (50143160)

Project Fiscal Year 
1998 – 2001

Project Status 
Completed(Fiscal Year 2001)

Budget Amount *help 
¥37,240,000 (Direct Cost : ¥34,300,000、Indirect Cost : ¥2,940,000)
Fiscal Year 2001 : ¥12,740,000 (Direct Cost : ¥9,800,000、Indirect Cost : ¥2,940,000)
Fiscal Year 2000 : ¥8,000,000 (Direct Cost : ¥8,000,000)
Fiscal Year 1999 : ¥8,000,000 (Direct Cost : ¥8,000,000)
Fiscal Year 1998 : ¥8,500,000 (Direct Cost : ¥8,500,000)

Keywords  Estimator / Test / Information amount / Sequential analysis / Multivariate analysis / Time series / Mathematical finance / Combinatorics / 推定量 / 検定 / 情報量 / 逐次解析 / 多変量解析 / 時系列 / 数理ファイナンス / 組合せ理論 / 計算機支援型推測 / 非正規性 / ノンパラメトリック推測 / 実験計画 / 時系列解析 / 金融 / 特異モデル / 最尤推定 / 非正則モデル / 有限標本論 / 統計的モデリング / ベイズ法 / 逐次推定 / 空間データ / 画像解析 / モデル選択 / ベイズ推測 / 推定 / 逐次推測 / 統計的モデル / 漸近有効性 
Research Abstract 
The statistical investigation on various themes was done as follows. (l)0n the statistical inference and its related topics, the inferential procedures were proposed and interesting results on the application were obtained. (2)0n the statistical nonregular theory, the properties of estimators were discussed, and new knowledges of the characterization of nonregular distributions were obtained. (3)0n the theory of inference and its information theoretic viewpoint, the structure of inference was clarified through amounts of information, and its relation to the theory of information was well investigated. (4)0n the fundamental theory to analyze the statistical model with prior informations and its applications, the optimality of inferential procedures was considered from the Bayesian point of view, and the results on possibility of the application to practical problems were obtained. (5)The space between multivariate analysis and time series was investigated in details, and new results on the
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comparison of inferential procedures were given. (6)0n the combinatoric design and its applications, the construction of experimental design was proposed and assessed. (7)0n the economic time series and mathematical finance, the construction of the fundamental theory of statistical inference was tried and its usefulness is investigated. (8)0n the multivariate analysis, the linear and nonlinear models were discussed, and new results on the inference were obtained in the nonregular case which was regarded as a difficult one. (9)The theoretical fundamentals and its applications were well investigated from the viewpoint of sequential analysis, and new results on the inferential procedures were obtained in the case of nonregular distributions. (10)0n the statistical and mathematical anakysis, new results on the efficiency of estimation and test procedures were given. In addition to the above, the results on the statistical modeling and inference, the spatial statistics, the recent computerassisted type inference and its applications and others were also obtained. Many symposiums on the above were held and active discussions and mutual exchanges of informations were also done. Their results were summarized as a book of about 800 pages. Less
