Study on theoretical framework of statistical methods

统计方法理论框架研究

• 批准号: 10480051
• 负责人: TAKEUCHI Kei
• 金额: $ 7.42万
• 依托单位: Meiji Gakuin University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B).
• 财政年份: 1998
• 资助国家: 日本
• 起止时间: 1998 至 2000
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-10480051/
• 关键词: Statistical prediction; Statistical applied decision theory; Non-stationary times series; Non-normal distribution; Statistical model selection; Non-parametric and semi-parametric methods; Non-regular estimation; 統計的決定理論; ノンパラメトリッフ法; 予測限界; ノンパラメト

Mathematical theory of statistical inference has been extensively developed in the last century, but in the last few decades it reached to more or less maturity, and theoretical research effort within the conventional framework now suffers diminishing rate of return. It is now required to try new directions of research, and this project was planned to review critically the present theoretical framework and to consider new formulations of theory and methods of statistical problems which are important in various fields of practical application.Statistical problems in various fields, such as clinical trials, human genome analysis, image processing, analysis of languages, financial engineering have been discussed. The common features of the problem we encounter in such fields are that we have a large amount of not uniformly controlled data, unlike small number of well controlled data in classical cases, and we cannot apply simply models characterized by few parameters to them. Also regularity conditions assumed in the classical theory often fail to hold, and various anomalies could happen. In such cases "optimum" or "best" solutions are usually difficult to be determined and we have to be satisfied with practically "workable" solutions. Also it is necessary to consider the real "objective" of practical data analysis, and "applied decision theory" approach must be taken into consideration.We got a number of results by the participants of the project, which have been and yet to be published in separate articles.

统计推断的数学理论在上个世纪得到了广泛的发展，但在过去的几十年里，它或多或少地达到了成熟，在传统框架内的理论研究工作现在遭受回报率递减。现在需要尝试新的研究方向，该项目计划批判性地审查目前的理论框架，并考虑在实际应用的各个领域都很重要的统计问题的理论和方法的新配方，在各个领域的统计问题，如临床试验，人类基因组分析，图像处理，语言分析，金融工程进行了讨论。我们在这些领域遇到的问题的共同特点是，我们有大量的不均匀控制的数据，不像在经典的情况下，控制良好的数据的数量很少，我们不能简单地应用模型的特点是很少的参数。此外，经典理论中假设的正则性条件往往不成立，各种异常可能发生。在这种情况下，“最佳”或“最佳”解决方案通常难以确定，我们必须满足于实际上“可行”的解决方案。此外，还必须考虑实际数据分析的真实的“目标”，必须考虑“应用决策理论”的方法。我们得到了该项目参与者的一些结果，这些结果已经和尚未发表在单独的文章中。

项目成果

Yasunori Fujikoshi: "Error Bounds for Asymptotic Approximation of the Liner Discriminant Function When the Sample Sizes and Dimensionality are Large"Journal of Multivariate Analysis. 73. 1-17 (2000)

Yasunori Fujikoshi：“样本量和维数很大时线性判别函数渐近逼近的误差界”多元分析杂志。

谷口正信 他: "Discrimination and Clustering for Multivariate Time Series"Journal of the American Statistical Association. Volume 93 Number 441. 329-340 (1998)

Masanobu Taniguchi 等人：“多元时间序列的判别和聚类”美国统计协会杂志第 93 卷第 441 期。329-340 (1998)

岸野洋久 他: "全国高齢者に対する12年間の縦断調査の脱落者・継続回答者の特性"日本公衆衛生雑誌. 第47巻. 337-349 (2000)

Hirohisa Kishino 等人：“全国老年人 12 年纵向调查中辍学和继续受访者的特征”，《日本公共卫生杂志》，第 47 卷，337-349（2000 年）。

竹内啓,赤平昌文: "Minimax Approach To Sequential Bernoulli Trials"Mathematical Research Note (Institute of Mathematic University of Tsukuba). 2000-011. (2000)

Kei Takeuchi、Masafumi Akahira：“序列伯努利试验的最小最大方法”数学研究笔记（筑波数学大学研究所）2000-011。

狩野 裕: "Delta method approach in a certain irregular condition"Communication in Statistic, Theoryaud Methods. 28-3,4. 789-807 (1999)

Yutaka Kano：“在某种不规则条件下的 Delta 方法”，《统计通讯》，Theoryaud 方法 28-3,4 (1999)。