Variable screening in multivariate linear regression with high-dimensional covariates

We propose two variable selection methods in multivariate linear regression with high-dimensional covariates. The first method uses a multiple correlation coefficient to fast reduce the dimension of the relevant predictors to a moderate or low level. The second method extends the univariate forward...

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Bibliographic Details
Published inStatistical theory and related fields Vol. 6; no. 3; pp. 241 - 253
Main Authors Bizuayehu, Shiferaw B., Li, Lu, Xu, Jin
Format Journal Article
LanguageEnglish
Published Taylor & Francis 26.08.2022
Taylor & Francis Group
Subjects
Dimension reduction
forward regression
multiple correlation coefficient
multivariate regression
variable selection
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Summary:We propose two variable selection methods in multivariate linear regression with high-dimensional covariates. The first method uses a multiple correlation coefficient to fast reduce the dimension of the relevant predictors to a moderate or low level. The second method extends the univariate forward regression of Wang [(2009). Forward regression for ultra-high dimensional variable screening. Journal of the American Statistical Association, 104(488), 1512-1524. https://doi.org/10.1198/jasa.2008.tm08516 ] in a unified way such that the variable selection and model estimation can be obtained simultaneously. We establish the sure screening property for both methods. Simulation and real data applications are presented to show the finite sample performance of the proposed methods in comparison with some naive method.
ISSN:2475-4269
2475-4277
DOI:10.1080/24754269.2021.1982607