Research on information extraction from complicated data using bootstrap or nonlinear optimization methods

在本研究中，开展了三种研究工作。取得的成果概述如下。首先，对于(A)Bootstrap相等性检验，提出了几种Bootstrap检验，并对其性质进行了数值检验，以考察成对纵向数据的平均差异。在所提出的检验统计量中，面积差统计量总体上似乎具有较好的性质，即权值最高，其次是平方差统计量。从检验能力的角度来看，这些统计量都优于传统的霍尔和哈特统计量。数值检验表明，即使在纵向数据相关性较弱和/或样本量较小的情况下，所提出的混合移动块重采样方法仍具有令人满意的效果。第二，对于(B)引导推理和对复杂实际数据的分析，我们考察了非课程测试所测得的能力。The…更多的测试意在测量逻辑思维能力、信息理解能力、交际能力和阅读理解能力。对问卷中的47个项目进行因素分析，得出6个因素反映了能力的不同方面。六个因素中有三个与非课程性考试显著相关。这些结果表明，这些测试项目可以测量预期的能力，如逻辑思维、阅读理解和相关能力，但交际能力除外。第三，对于参数估计中的(C)非线性优化问题及其稳定性，在多元回归分析的情况下，我们解析地得到了在二次和线性约束下最大化相关的最优解。然后，我们研究了典型相关分析情况下的最优解，并应用在多元回归情况下发展起来的迭代方法得到了最优解。迭代法被证明是有限步停止的。我们还考察了最优解的稳定性，结果表明，即使数据值有很小的变化，最优解也可能发生灾难性的变化。较少

In this study, three kind of research works were carried out. The outline of the obtained results are as follows. First, as for (A) bootstrap equality tests, several bootstrap tests were proposed and the properties were numerically examined in order to investigate the mean difference of paired longitudinal data. Among proposed test statistics, area difference statistic seemed to have good property on the whole ; that is the power is highest, and the squared difference statistic followed. These statistics were better than the traditional ones, for example Hall ＆ Hart statistic, from the viewpoint of the test power. By numerical examination, the proposed mixed moving block resampling method had satisfactory power even in the situations where the correlation between longitudinal data was rather week and/or the sample size was fairly small. Second, as for (B) bootstrap inference and analysis of complicated actual data, we investigated the ability measured by non-curriculum-based test. The … More test was developed to intend to measure logical thinking, information apprehension ability, communicative competence and reading comprehension ability. Factor analysis of 47 items included in the questionnaire yielded six factors reflecting different aspects of abilities. Three of the six factors significantly correlated with the non-curriculum-based test. These results imply that the test items could measure the intended abilities, such as logical thinking, reading comprehension and related abilities, except for communicative competence. Third, as for (C) nonlinear optimization problems in parameter estimation and its stability, we analytically obtained the optimal solution which maximized correlation under quadratic and linear constraints in case of multiple regression analysis. We then investigated the optimal solution in case of canonical correlation analysis, and derived it by applying the technique iteratively which was developed in multiple regression case. The iterative method was proved to stop by finite steps. The stability of the optimal solution was also examined, and we showed the possibility that the solution changed catastrophically even for the small change of data values. Less