Study on theoretical framework of statistical methods

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的程度，传统框架内的理论研究成果现在正遭受着回报率的下降。现在需要尝试新的研究方向，这个项目计划批判性地审查现有的理论框架，考虑在实际应用的各个领域中重要的统计问题的理论和方法的新公式。讨论了临床试验、人类基因组分析、图像处理、语言分析、金融工程等不同领域的统计问题。我们在这些领域中遇到的问题的共同特征是，我们拥有大量的非均匀控制数据，而不像经典情况下的少量良好控制的数据，我们不能简单地对它们应用参数较少的模型。此外，经典理论中假设的正则性条件往往不成立，可能会发生各种反常情况。在这种情况下，“最佳”或“最佳”解决方案通常很难确定，我们必须满足于实际“可行”的解决方案。此外，还必须考虑实际数据分析的真正“目标”，并必须考虑“应用决策理论”的方法。我们从项目参与者那里获得了一些结果，这些结果已经发表在单独的文章中，但尚未发表。

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.