| Project/Area Number |
16500171
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Statistical science
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| Research Institution | The National Center for University Entrance Examinations (2005-2006)
Chiba University (2004) |
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Principal Investigator |
TAGURI Masaaki The National Center for University Entrance Examinations, Professor, 研究開発部, 教授 (10009607)
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| Co-Investigator(Kenkyū-buntansha) |
NAKAMURA Katsuhiro Chiba University, Faculty of Science, Professor, 理学部, 教授 (10344962)
NAKAGAMI Junichi Chiba University, Faculty of Science, Professor, 理学部, 教授 (30092076)
MIYANO Hisao Chiba University, Faculty of Letters, Professor, 文学部, 教授 (90200196)
WANG Jinfang Chiba University, Graduate School of Science and Technology, Associate Professor, 大学院自然科学研究科, 助教授 (10270414)
SAKURAI Hirohito Hokkaido University, Graduate School of Engineering, Assistant Professor, 大学院工学研究科, 助手 (00333625)
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| Project Period (FY) |
2004 – 2006
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| Project Status |
Completed (Fiscal Year 2006)
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| Budget Amount *help |
¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 2006: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2005: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2004: ¥1,500,000 (Direct Cost: ¥1,500,000)
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| Keywords | test of difference of two mean curves / bootstrap test / area difference test statistic / block resampling / non-curriculum-based ability test / optimization of correlation coefficient / canonical correlation analysis / quadratic constraint / 縦断的データ / 混合ブロックリサンプリング / 並べ替え検定 / 総合試験 / 経時的データ / 混合ブートストラップ検定 / パーミュテーション検定 / 検定のサイズとパワー / 面積検定統計量 / 差の絶対値統計量 / 差の2乗和統計量 / Hall&Hartの統計量 / 検定のサイズと検出力 |
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| Research Abstract |
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
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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
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