2021 Fiscal Year Final Research Report
A fast and simple consistent variable selection method for high-dimensional multivariate data
| Project/Area Number |
18K03415
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Review Section |
Basic Section 12040:Applied mathematics and statistics-related
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| Research Institution | Hiroshima University |
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Principal Investigator |
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| Project Period (FY) |
2018-04-01 – 2022-03-31
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| Keywords | 変数選択 / 多変量線形回帰モデル / 一致性 / 有効性 / 高次元漸近理論 / 情報量規準 |
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| Outline of Final Research Achievements |
We proposed a fast and simple consistent variable selection method in multivariate linear regression models when the numbers of response and explanatory variables are large. The decision whether an explanatory variable is necessary or not is based on the difference between the model selection criteria of the full model and a candidate model in which only the target explanatory variable is removed. The consistency of the model selection criterion used was evaluated using asymptotic theory, in which the sample size goes to infinity under the condition that the sum of the numbers of response and explanatory variables divided by the sample size converges to a constant less than 1. By guaranteeing the consistency with this asymptotic theory, we could propose a variable selection method that is expected to increase the probability of selecting the true explanatory variables regardless of the sizes of the numbers of response and explanatory variables if the sample size is large enough.
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| Free Research Field |
統計科学
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| Academic Significance and Societal Importance of the Research Achievements |
本研究課題で提案する変数選択法は，ある程度大きい標本数があれば，目的変数や説明変数の個数の大小にかかわらず，選択確率が高くなると期待できる．よって，提案手法は，既存の変数選択法と一線を画す，計算時間が短く目的変数や説明変数の個数の大小によらないuser friendlyな手法であると言える． また，他の多変量解析法の変数選択法に拡張できる可能性があることから，提案手法は汎用性も高い変数選択法になることも期待できる．以上のことから，提案する変数選択法は現在広く利用されているスパース推定に基づく変数選択法に替わる標準的な手法になる可能性を秘めていると言える．
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