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 relevant predictors moderate or low level. second extends univariate forward Wang [(2009). Forward for ultra-high dimensional screening. Journal American Statistical Association, 104(488), 1512–1524. https://doi.org/10.1198/jasa.2008.tm08516] unified way such that and model estimation can be obtained simultaneously. establish sure screening property both methods. Simulation real data applications are presented show finite sample performance proposed comparison some naive method.