Forward Regression for Ultra-High Dimensional Variable Screening
研究了前向回归在超高维变量筛选中的理论性质，证明其能一致识别所有相关预测变量，并可与BIC准则及SCAD、自适应Lasso等方法结合使用。
Motivated by the seminal theory of Sure Independence Screening (Fan and Lv 2008, SIS), we investigate here another popular and classical variable screening method, namely, forward regression (FR). Our theoretical analysis reveals that FR can identify all relevant predictors consistently, even if the predictor dimension is substantially larger than the sample size. In particular, if the dimension of the true model is finite, FR can discover all relevant predictors within a finite number of steps. To practically select the “best” candidate from the models generated by FR, the recently proposed BIC criterion of Chen and Chen (2008) can be used. The resulting model can then serve as an excellent starting point, from where many existing variable selection methods (e.g., SCAD and Adaptive LASSO) can be applied directly. FR’s outstanding finite sample performances are confirmed by extensive numerical studies.