Prediction Consistency of Forward Iterated Regression and Selection Technique

Recently, Hwang et al. (2009) proposed a variable selection method for high dimensional linear regression by attaching a penalty term with the loss function in a forward selection scheme, and regulate stopping by the amount of improvement in the loss function. The method ap-pears to possess excellent prediction and variable selection property, but thus far no theoretical result on the procedure is given. In this article, we show that the procedure is prediction consistent