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Theory and application of information extraction in mathematical statistics

数理统计信息提取理论与应用

基本信息

批准号：
08304015
负责人：
TAGURI Masaaki
金额：
$ 11.39万
依托单位：
Chiba University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (A)
财政年份：
1996
资助国家：
日本
起止时间：
1996 至 1997
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-08304015/
关键词：
Statistical analysis of chaotic, nonlinear data Multivariate analysis and its asymptotic theory Mathematical programming model and its optimization Time series analysis and its asymptotic theory Sequential analysis Distribution theory and statis

项目摘要

In this research, we investigated the theory of information extraction in mathematical statistics and applied the results to various kinds of practical data-set. 11 special topics were selected and research sympojiums were held on each topic. As a result, new theories and methodologies were developed and useful knowledges were obtained in many practical fields. Statistical software were also constructed. Through discussions in sympojiums and meetings, further problems were pointed out. Main results obtained in 11 sympojiums were as follows :(1) Development of the theories and methodologies for analyzing complicated nonlinear data and investigation on the limit in practical use.(2) Research of descriptive statistics and statistical inference on multivariate analysis, and the understanding of their discrepancy.(3) Development of optimization theories in mathematical programming and model construction for applying the results to practical problems.(4) Investigation on asymptotic theory, large deviation theory, model selection in time series analysis and their application.(5) Investigation on the theories and methodologies of sample sizes in sequential analysis required to carry out efficient statistical inference.(6) Investigation on probability distributions and sampling distributions concerning various statistical models.(7) Investigation on combinatorial mathematics, integral conditions and optimization in statistical model construction and inference.(8) Development of the theories on computer-intensive statistical methods and construction of useful statistical software.(9) Development of statistical asymptotic theory and construction of the computer-intensive algorithms.(10) Investigation on statistical inference concerning multivariate model, stochastic process model, time siries model and Baysian model.(11) Construction of good estimators and joint confidence intervals, and investigation on their properties.

在本研究中，我们对数理统计中的信息提取理论进行了探讨，并将研究结果应用于各种实际数据集。选择了11个专题，并就每个专题举行了研究研讨会。因此，新的理论和方法得到了发展，并在许多实际领域获得了有用的知识。并编制了统计软件。通过专题讨论会和会议的讨论，指出了进一步的问题。11次专题讨论会取得的主要成果如下：(1)发展了复杂非线性数据分析的理论和方法，探讨了实际应用中的极限。(2)多变量分析的描述性统计和统计推断研究及其差异理解。(3)发展数学规划中的优化理论和模型构建，将结果应用于实际问题。(4)时间序列分析中的渐近理论、大偏差理论、模型选择及其应用研究。(5)对序贯分析中样本量的理论和方法进行研究，以便进行有效的统计推断。(6)研究各种统计模型的概率分布和抽样分布。(7)统计模型构建与推理中的组合数学、积分条件与优化研究。(8)计算机密集型统计方法理论的发展和实用统计软件的建设。(9)统计渐近理论的发展和计算机密集型算法的构建。（10）多元模型、随机过程模型、时间序列模型和贝叶斯模型的统计推断研究。（11）良好估计量和联合置信区间的构造及其性质的研究。