2021 Fiscal Year Final Research Report
Studies on general and nearly exact statistical methods for monotone missing data under nonnormality and their applications
| 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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| Keywords | 欠測データ / 楕円分布族 / 仮説検定 / 尤度比検定 / 判別分析 |
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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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| Free Research Field |
数理統計学
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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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