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2020 A fast and consistent variable selection method for high-dimensional multivariate linear regression with a large number of explanatory variables
Ryoya Oda, Hirokazu Yanagihara
Electron. J. Statist. 14(1): 1386-1412 (2020). DOI: 10.1214/20-EJS1701

Abstract

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.

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Ryoya Oda. Hirokazu Yanagihara. "A fast and consistent variable selection method for high-dimensional multivariate linear regression with a large number of explanatory variables." Electron. J. Statist. 14 (1) 1386 - 1412, 2020. https://doi.org/10.1214/20-EJS1701

Information

Received: 1 March 2019; Published: 2020
First available in Project Euclid: 28 March 2020

zbMATH: 07200232
MathSciNet: MR4080281
Digital Object Identifier: 10.1214/20-EJS1701

Subjects:
Primary: 62J05
Secondary: 62E20

Keywords: consistency , high-dimensional asymptotic framework , multivariate linear regression , Variable selection

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Vol.14 • No. 1 • 2020
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