Multivariate normality test, and inference for variable selection in high-dimensional model and its applications
| Project/Area Number |
15K15953
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Statistical science
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| Research Institution | Seikei University (2018-2019)
Tokyo University of Science (2015-2017) |
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Principal Investigator |
Enomoto Rie 成蹊大学, 理工学部, 助教 (30711767)
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| Project Period (FY) |
2015-04-01 – 2020-03-31
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| Project Status |
Completed (Fiscal Year 2019)
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| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 統計科学 / 多変量解析 |
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| Outline of Final Research Achievements |
In this study, tests for multivariate normality (MVN) of Jarque-Bera type, based on skewness and kurtosis, have been considered. Simulation results have been compared to the Henze-Zirkler's test. In the Monte Carlo simulations, we calculated empirical Type I errors of tests under consideration, and empirical power against different alternative distributions.
In this study, we derived consistency properties for variable selection methods based on model selection criteria in growth curve model. The model selection criteria treated includes AIC criterion, BIC criterion and Cp criterion, or their modified criteria. The properties were derived under a high-dimensional asymptotic framework and a large-(q;n) asymptotic frame work such that the ratio of the number of group to the sample size tends to afixed number less than 1.
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| Academic Significance and Societal Importance of the Research Achievements |
昨今，データが一般に手に入りやすくなったこともあり，分析手法に正規性の仮定が必要である場合にはまず分析をする前にデータを吟味する必要がある．また，変数の次元が大きい場合の統計的方法や多量の変数の中から有用な変数を選び出す変数選択方法には高い需要が生まれてきている．これらはデータ分析における重要な課題であることから基礎研究に限らず，その応用研究にも取り組むことで統計科学における理論や応用に対する貢献が期待される．
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Report
(6 results)
Research Products
(8 results)
