Variable screening in multivariate linear regression with high-dimensional covariates. Issue 3 (26th August 2022)

• Record Type: Journal Article
• Authors: Bizuayehu, Shiferaw B.; Li, Lu; Xu, Jin
• Is Part Of: Statistical theory and related fields. Volume 6:Issue 3(2022)
• Page Start: 241
• Page End: 253
• Publication Date: 2022-08-26
• Subjects: Dimension reduction -- forward regression -- multiple correlation coefficient -- multivariate regression -- variable selection; Statistics -- Periodicals; Statistics; Periodicals; Electronic journals; 001.422
• DOI: 10.1080/24754269.2021.1982607
• Languages: English
• ISSNs: 2475-4269

Abstract

Abstract : 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.