Development of consistent variable selection criteria with high-dimensional response and explanatory variables using forward-backward stepwise selection method

2023 Fiscal Year Final Research Report

• Project/Area Number: 20K14363
• Research Category: Grant-in-Aid for Early-Career Scientists
• Allocation Type: Multi-year Fund
• Review Section: Basic Section 12040:Applied mathematics and statistics-related
• Research Institution: Hiroshima University
• Principal Investigator: Oda Ryoya 広島大学, 先進理工系科学研究科(理), 助教 (10853682)
• Project Period (FY): 2020-04-01 – 2024-03-31
• Keywords: 多変量モデル / モデル選択 / 一致性 / 高次元

Outline of Final Research Achievements

The aim of this study is to propose a variable selection criterion with good properties for high-dimensional and large-sample data in multivariate models, including cases where the number of dimensions of the variables exceeds the sample size. In particular, we propose a criterion with consistency, which is the property that the probability of selecting the true variable is asymptotically one under a high-dimensional setting where the number of variables may exceed the sample size. In order to achieve the aim, we evaluate the consistency in multivariate models under the high-dimensional asymptotic theory, in which the sample size is infinite but the number of variables may be infinite, and propose a variable selection method with consistency.

Free Research Field

数理統計

Academic Significance and Societal Importance of the Research Achievements

近年では高次元データの使用は頻繁にされるため, そのような高次元データに対する統計分析手法の開発は重要である. 本研究により提案された変数選択手法は高次元データに対しても良い性質をもちかつ計算も高速であるため, リーズナブルな手法であると考えられる.