| Project/Area Number |
19K14595
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| Research Category |
Grant-in-Aid for Early-Career Scientists
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| Allocation Type | Multi-year Fund |
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| Review Section |
Basic Section 12040:Applied mathematics and statistics-related
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| Research Institution | Kindai University (2020-2021)
Kobe University (2019) |
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Principal Investigator |
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| Project Period (FY) |
2019-04-01 – 2022-03-31
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| Project Status |
Completed (Fiscal Year 2021)
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| Budget Amount *help |
¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2021: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2020: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2019: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 欠測データ / 楕円分布族 / 仮説検定 / 尤度比検定 / 判別分析 / 変数選択 / 漸近展開 / 検出力 / 非正規母集団 / 統計的漸近理論 / Bartlett型修正 |
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| Outline of Research at the Start |
本研究課題では，対称な分布族として知られる楕円分布族を母集団分布とし，その母集団から得られた単調欠測データを基にした多変量統計解析法を提案する．特に，実用上重要であると考えられる統計解析法（平均ベクトルに関する仮説検定，判別分析等）に着目し，母集団分布の確率密度関数や，欠測が生じる確率モデル（欠測データメカニズム）についての制約を緩めた下で，高い汎用性と精度を保つ統計解析法の提案を行う．また，提案する仮説検定方式の検出力や判別規準の誤判別確率に対する高精度な近似式も併せて導出することにより，標本サイズの設計や非正規性の影響に関わる重要な知見を得ることも目指す．
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| Outline of Final Research Achievements |
In this research, assuming that missing datasets were drawn from the elliptically contoured distributions including some non-normal distributions, we considered the statistical analysis which could be applied to the datasets. In these settings, our goal was to obtain the statistical analysis which performed well even if the sample size was not so large and to consider the applications to the real datasets. In particular, we focused on missing data whose missing patterns were monotone type owing to dropouts and obtained the following results: (i) the likelihood ratio based test for a mean vector and its Bartlett-type correction, (ii) the approximated power of the test stated in (i), and (iii) the likelihood ratio test for the redundancy of the variables in linear discriminant analysis and its simulation studies.
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| Academic Significance and Societal Importance of the Research Achievements |
本研究成果は，データの多様化に対応すべく，多変量正規分布および対称な非正規分布を含む分布族（楕円分布族）から得られた欠測データに対して適用可能な統計解析法を求めるものである．特に，平均ベクトルに対する仮説検定や，どの変量がデータ解析に必要となるかを解析する冗長性検定は関心がもたれることが多いため，これらの検定問題に対する検定統計量の導出，理論的修正，および数値的考察を与えた．
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