文章基本信息

标题：A fast and consistent variable selection method for high-dimensional multivariate linear regression with a large number of explanatory variables
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作者：Ryoya Oda ; Hirokazu Yanagihara
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2020
卷号：14
期号：1
页码：1386-1412
DOI：10.1214/20-EJS1701
语种：English
出版社：Institute of Mathematical Statistics
摘要：We put forward a variable selection method for selecting explanatory variables in a normality-assumed multivariate linear regression. It is cumbersome to calculate variable selection criteria for all subsets of explanatory variables when the number of explanatory variables is large. Therefore, we propose a fast and consistent variable selection method based on a generalized $C_{p}$ criterion. The consistency of the method is provided by a high-dimensional asymptotic framework such that the sample size and the sum of the dimensions of response vectors and explanatory vectors divided by the sample size tend to infinity and some positive constant which are less than one, respectively. Through numerical simulations, it is shown that the proposed method has a high probability of selecting the true subset of explanatory variables and is fast under a moderate sample size even when the number of dimensions is large.
关键词：Consistency; high-dimensional asymptotic framework; multivariate linear regression; variable selection