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

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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