One fundamental ingredient of our work is to formally split the signals into strong and weak ones. The rationale is that the usual one-step method such as the least absolute shrinkage and selection operator (LASSO) may be very effective in detecting strong signals while failing to identify some weak ones, which in turn has a significant impact on the model fitting, as well as prediction. The discussions of both Fan and QYY contain very interesting comments on the separation of the three sets of variables. Regarding Assumption (A2) about the weak signal set S2, we admit that the original version was not as rigorous as it could have been, as it could have contained the variables in S3. We now propose the following Assumption (A2') that replaces (A2) in the original paper.
