Theory and application of information extraction in mathematical statistics

本研究探讨数理统计中的资讯撷取理论，并将其应用于各种实际资料。选择了11个专题，并就每个专题举行了研究座谈会。因此，新的理论和方法被开发，并在许多实际领域获得了有用的知识。还开发了统计软件。通过专题讨论会和会议的讨论，指出了进一步的问题。（1）发展了分析复杂非线性数据的理论和方法，并对实际应用中的极限问题进行了探讨。(2)多元分析之描述统计与统计推论之研究及其差异之理解。(3)发展数学规划中的最优化理论，并将结果应用于实际问题的模型构建。(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)研究序贯分析中样本容量的理论和方法，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)研究统计模型建构与推论之组合数学、积分条件与最佳化。(8)计算机密集型统计方法理论的发展和实用统计软件的构建。(9)统计渐近理论的发展和计算机密集型算法的构建。(10)研究了多元模型、随机过程模型、时序模型和贝叶斯模型的统计推断。(11)构造好的估计量和联合置信区间，并研究它们的性质。

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.